Commercial Fixed Wing
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 10
Distraction; Confusion; Communication Breakdown; Situational Awareness
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Environment - Non Weather Related; Procedure; Human Factors
Aircraft X was IFR inbound to ZZZ requesting the LOC RWY XX; however; the tower still on their COVID hours closes early. When the tower closed they put the localizer on RWY YY so the LOC RWY XX was unavailable. Due to winds Aircraft X was unable RWY YY. They requested the RNAV Y RWY XX. I had traffic for Aircraft X as they were approaching ZZZZZ with the crossing altitude of 051 and the traffic at 047 I gave a restriction for traffic. This confused the pilot so I went back and cancelled the approach clearance and told the pilot to expect clearance at ZZZZZ1; but this was a mistake; what I meant to say was ZZZZZ. The pilot did not question me but did seem confused. Rightfully so. When Aircraft X was clear of the traffic they reported that they were direct ZZZZZ. I then cleared Aircraft X to cross ZZZZZ at 5;100 cleared straight in RNAV Y Rwy XX approach. Aircraft X appeared to over shoot ZZZZZ before turning to ZZZZZ2. I questioned the pilot that the next fix past ZZZZZ was ZZZZZ2; is that where they show their self going. The pilot stated they just passed ZZZZZ2 and I can't quite understand what they said after that. But at the time I thought they said going to ZZZZZ3 the next fix on the approach. While this was going on I had a couple other aircraft waiting and another facility call me for point outs. When my attention took me back to Aircraft X their path appeared off and had began a go around and the moment they called me I issued the low altitude alert and an immediate climb. They attempted the approach and landed safely on the second attempt. My initial reaction to this approach was that something was off; which is when I questioned the pilot. I gave them the benefit of the doubt and hoped that they had corrected the overshoot at ZZZZZ and was properly on the RNAV Y RWY XX at ZZZ. However; I should have just gone with my gut and broke the aircraft off the approach when I noticed the error and vectored back around for a second attempt. Hindsight when you look back is always better. We try to not delay aircraft and hope that they are truthful when we question them about approaches. However; safety is our number one priority and concern and I did feel like there was something not right and looking back I wish I would have just broken the aircraft off the approach and re-sequenced. It is always easier to watch a replay to see how we can improve; but that is important so we do not repeat our mistakes.
TRACON Controller reported having an aircraft that wanted one approach; but the tower was closed and the approaches were set up for the opposite direction.  Controller reported possibly confusing pilot with clearances.