user8157: 
Abhidhammabhājanīya says:


2.1. Paccayacatukka
27.1Avijjāpaccayā saṅkhāro, saṅkhārapaccayā viññāṇaṁ, viññāṇapaccayā nāmaṁ, nāmapaccayā chaṭṭhāyatanaṁ, chaṭṭhāyatanapaccayā phasso, phassapaccayā vedanā, vedanāpaccayā taṇhā, taṇhāpaccayā upādānaṁ, upādānapaccayā bhavo, bhavapaccayā jāti, jātipaccayā jarāmaraṇaṁ. 27.2Evametassa kevalassa dukkhakkhandhassa samudayo hoti
With ignorance as condition there is a (volitional) process, with a (volitional) process as condition: consciousness, with consciousness as condition: mind, with mind as condition: the sixth sense sphere, with the sixth sense sphere as condition: contact, with contact as condition: feeling, with feeling as condition: craving, with craving as condition: attachment, with attachment as condition: continuation, with continuation as condition: birth, with birth as condition: ageing, death, and so there is an origination of this whole mass of suffering.
28.1 Avijjāpaccayā saṅkhāro, saṅkhārapaccayā viññāṇaṁ, viññāṇapaccayā nāmaṁ, nāmapaccayā phasso, phassapaccayā vedanā, vedanāpaccayā
taṇhā, taṇhāpaccayā upādānaṁ, upādānapaccayā bhavo, bhavapaccayā jāti,
jātipaccayā jarāmaraṇaṁ. 28.2Evametassa kevalassa dukkhakkhandhassa
samudayo hoti
With ignorance as condition there is a (volitional) process, with a (volitional) process as condition: consciousness, with consciousness as condition: mind, with mind as condition: contact, with contact as condition: feeling, with feeling as condition: craving, with craving as condition: attachment, with attachment as condition: continuation, with continuation as condition: birth, with birth as condition: ageing, death, and so there is an origination of this whole mass of suffering.
https://suttacentral.net/vb6/pli/ms#pts-cs251

What is the sense contact (phasso) occurring without a sense base or sense organ & sense object (āyatana)?

user16323: Mind is the sixth ayatana. Contact here would be contact with a mind object, like a thought. The OP question is poorly framed in suggesting there is no ayatana involved here, since it is clearly about the mano (mind) ayatana .

user43: DO describes development of defiled subjective world, defiled mind and defiled sense of self.
"nama" is an idea of an object, a concept, a mental label. For example, when an infant sees the mother there's recognition: "it is She". The infant does not yet know how to speak, it has no words, but the recognizing consciousness (vijnana) begins to develop, and once it can recognize the mother there's a "nama" of mother, a notion of that particular object.
As the developing vijnana establishes more and more notions of visual objects, the idea of "seeing" begins to emerge. As the developing vijnana establishes more and more notions of audial objects, the idea of "hearing" begins to emerge. And so on for other senses. As the developing vijnana establishes more and more notions of mental objects, the idea of "thinking" begins to emerge. Until you see enough objects, you don't know you could see. Until you hear enough sounds, you don't know you could hear. Until you have enough thoughts, you don't know you could think.
Once these developments are complete and there's a fully developed recognizing consciousness, a notion of object, and a notion of seeing, hearing, thinking etc., - there can be established a notion of "contact" on a sensory modality.
Even though infant has "seen" the mother a million times before that, there's no contact until there's both a notion of mother and a notion of seeing. Once all of these are complete, there's a notion "I see mother". That's the contact. The infant cannot speak but it knows when it sees the mother, hears the mother, smells the mother.
Coming back to your question, that particular example explains development of the sixth modality, the modality of thinking, inner attention, inner representation, inner recognition. What we call mentation. In this modality our recognizing consciousness delineates inner objects such as "thoughts" and "memories", establishes their identities ("nama"), and once enough of these have been established there emerges a notion of "inner space", followed by the notion "I'm having this thought" or "I'm having this memory" - i.e. the mental contact.
As you can see, a particular instance of mental contact can occur without another sense organ being involved at all. But of course in the larger context we understand that in the human world a development of the sixth sense with its inner objects does not occur in the total absence of any external stimuli. After all, it is the visual consciousness and other sensory consciousnesses that provide food for the mental consciousness to chew on.
Nevertheless the point of that Abhidharma passage is to emphasize that the sixth sense or the mental modality undergoes its own development process - establishing its mental objects, its mental context, recognizing the contact with a mental object, pleasure or pain resulting from the contact with a mental object, craving for a contact with a mental object, sustaining an attitude towards a mental object, becoming the owner of an attitude towards a mental object, establishing a notion of self as the owner of a collection of certain attitudes.

8157: <ol start="2">
<li>Abhidhammabhājanīya says:</li>
</ol>
<blockquote>
<p>2.1. Paccayacatukka</p>
<p>27.1Avijjāpaccayā saṅkhāro, saṅkhārapaccayā viññāṇaṁ, viññāṇapaccayā nāmaṁ, nāmapaccayā chaṭṭh<strong>āyatana</strong>ṁ, chaṭṭhāyatanapaccayā phasso, phassapaccayā vedanā, vedanāpaccayā taṇhā, taṇhāpaccayā upādānaṁ, upādānapaccayā bhavo, bhavapaccayā jāti, jātipaccayā jarāmaraṇaṁ. 27.2Evametassa kevalassa dukkhakkhandhassa samudayo hoti</p>
<p>With ignorance as condition there is a (volitional) process, with a (volitional) process as condition: consciousness, with consciousness as condition: mind, with mind as condition: the sixth <strong>sense sphere</strong>, with the sixth sense sphere as condition: contact, with contact as condition: feeling, with feeling as condition: craving, with craving as condition: attachment, with attachment as condition: continuation, with continuation as condition: birth, with birth as condition: ageing, death, and so there is an origination of this whole mass of suffering.</p>
<p>28.1 Avijjāpaccayā saṅkhāro, saṅkhārapaccayā viññāṇaṁ, viññāṇapaccayā nāmaṁ, <strong>nāmapaccayā phasso</strong>, phassapaccayā vedanā, vedanāpaccayā
taṇhā, taṇhāpaccayā upādānaṁ, upādānapaccayā bhavo, bhavapaccayā jāti,
jātipaccayā jarāmaraṇaṁ. 28.2Evametassa kevalassa dukkhakkhandhassa
samudayo hoti</p>
<p>With ignorance as condition there is a (volitional) process, with a (volitional) process as condition: consciousness, with consciousness as condition: mind, <strong>with mind as condition: contact</strong>, with contact as condition: feeling, with feeling as condition: craving, with craving as condition: attachment, with attachment as condition: continuation, with continuation as condition: birth, with birth as condition: ageing, death, and so there is an origination of this whole mass of suffering.</p>
<p><a href="https://suttacentral.net/vb6/pli/ms#pts-cs251" rel="nofollow noreferrer">https://suttacentral.net/vb6/pli/ms#pts-cs251</a></p>
</blockquote>
<p>What is the sense contact (phasso) occurring without a sense base or sense organ &amp; sense object (āyatana)?</p>
 16323: <p>Mind is the sixth ayatana. Contact here would be contact with a mind object, like a thought. The OP question is poorly framed in suggesting there is no ayatana involved here, since it is clearly about the mano (mind) ayatana .</p>
 43: <p>DO describes development of defiled subjective world, defiled mind and defiled sense of self.</p>
<p>&quot;nama&quot; is an idea of an object, a concept, a mental label. For example, when an infant sees the mother there's recognition: &quot;it is She&quot;. The infant does not yet know how to speak, it has no words, but the recognizing consciousness (vijnana) begins to develop, and once it can recognize the mother there's a &quot;nama&quot; of mother, a notion of that particular object.</p>
<p>As the developing vijnana establishes more and more notions of visual objects, the idea of &quot;seeing&quot; begins to emerge. As the developing vijnana establishes more and more notions of audial objects, the idea of &quot;hearing&quot; begins to emerge. And so on for other senses. As the developing vijnana establishes more and more notions of mental objects, the idea of &quot;thinking&quot; begins to emerge. Until you see enough objects, you don't know you could see. Until you hear enough sounds, you don't know you could hear. Until you have enough thoughts, you don't know you could think.</p>
<p>Once these developments are complete and there's a fully developed recognizing consciousness, a notion of object, and a notion of seeing, hearing, thinking etc., - there can be established a notion of &quot;contact&quot; on a sensory modality.</p>
<p>Even though infant has &quot;seen&quot; the mother a million times before that, there's no contact until there's both a notion of mother and a notion of seeing. Once all of these are complete, there's a notion &quot;I see mother&quot;. That's the contact. The infant cannot speak but it knows when it sees the mother, hears the mother, smells the mother.</p>
<p>Coming back to your question, that particular example explains development of the sixth modality, the modality of thinking, inner attention, inner representation, inner recognition. What we call mentation. In this modality our recognizing consciousness delineates inner objects such as &quot;thoughts&quot; and &quot;memories&quot;, establishes their identities (&quot;nama&quot;), and once enough of these have been established there emerges a notion of &quot;inner space&quot;, followed by the notion &quot;I'm having this thought&quot; or &quot;I'm having this memory&quot; - i.e. the mental contact.</p>
<p>As you can see, a particular instance of mental contact can occur without another sense organ being involved at all. But of course in the larger context we understand that in the human world a development of the sixth sense with its inner objects does not occur in the total absence of any external stimuli. After all, it is the visual consciousness and other sensory consciousnesses that provide food for the mental consciousness to chew on.</p>
<p>Nevertheless the point of that Abhidharma passage is to emphasize that the sixth sense or the mental modality undergoes its own development process - establishing its mental objects, its mental context, recognizing the contact with a mental object, pleasure or pain resulting from the contact with a mental object, craving for a contact with a mental object, sustaining an attitude towards a mental object, becoming the owner of an attitude towards a mental object, establishing a notion of self as the owner of a collection of certain attitudes.</p>
