user100257: Is it possible to make a transaction with no transaction fee? Is it possible to pay more fee to prioritize your transaction? 

user13866: 
Is it possible to make a transaction with no transaction fee?

As Raghav Sood noted in a comment, transactions with no transaction fee are not transmitted by standard Bitcoin nodes - so your zero-fee transaction normally won't reach a miner. In theory you could make some special arrangement with a miner but it's hard to see why they would want to do that.

Is it possible to pay more fee to prioritize your transaction?

Choosing a higher initial fee tends to result in quicker confirmation. If your wallet supports Replace By Fee (RBF) you can use that subsequently to improve the likelihood of a quicker confirmation.

100257: <p>Is it possible to make a transaction with no transaction fee? Is it possible to pay more fee to prioritize your transaction? </p>
 13866: <blockquote>
  <p>Is it possible to make a transaction with no transaction fee?</p>
</blockquote>

<p>As Raghav Sood noted in a comment, transactions with no transaction fee are not transmitted by standard Bitcoin nodes - so your zero-fee transaction normally won't reach a miner. In theory you could make some special arrangement with a miner but it's hard to see why they would want to do that.</p>

<blockquote>
  <p>Is it possible to pay more fee to prioritize your transaction?</p>
</blockquote>

<p>Choosing a higher initial fee tends to result in quicker confirmation. If your wallet supports <a href="https://en.bitcoin.it/wiki/Replace_by_fee" rel="nofollow noreferrer">Replace By Fee (RBF)</a> you can use that subsequently to improve the likelihood of a quicker confirmation.</p>
