My father is helping his godson re-finance his mortgage. Evidently the mortgage company wants proof that my father paid off his own mortgage which he did 20+ years ago. He cannot remember where he put the deed after it was mailed to him. What is the easiest way to go about getting another deed in Dallas County?

Sounds like you are looking for a Release of Lien. Nonetheless, if you want to obtain documents online, you could either search the county's clerks records website directly (in this case, https://dallas.tx.publicsearch.us/) or use the Texas File website (https://www.texasfile.com/).

I believe Dallas County charges $1 per document (for an official copy) if you get the doc from their website. I just checked and Texas File and it does have deeds and some related documents for Dallas County. To download a legal copy of a document you find there, you will have to pay a fee too (usually $2 per document).

Of course, you could also just go to the clerks office in person too.