Deductions & credits

What your daughter financed is not relevant. It just doesn't matter where she got the money she paid you -- a mortgage, investments, etc.

You have what's called a partial sale and partial gift.

The income tax rules for such gift/sales are here:

https://www.law.cornell.edu/cfr/text/26/1.1015-4

(the rules for a straight gift are at https://www.law.cornell.edu/cfr/text/26/1.1015-1)

Tell us a little more and we can help you more with the income tax consequences to you and to your daughter should she sell the property in the future. In particular:

1. What is your adjusted basis in the property? (I.e. what was your original purchase price plus and capital improvements - e.g. renovations, additions)
2. Have you owned and lived in the property for at least 2 of the last 5 years?
3. Did you own the house with your spouse? If so how ("joint tenancy" is the most common)? Is your spouse still living? If not what was the fair-market value of the home when your spouse passed?

BTW, getting an appraisal rather than just using the town's assessed value was very smart. An appraisal from a licensed appraiser will be much more reliable and will withstand scrutiny much better.

If the amount of equity you gifted to your daughter is more than the gift tax annual exclusion ($15k in 2021, $16k in 2022), then you will have to file a gift tax return (Form 709). If you are married you can usually double those amounts.  It would appear that your gift would be valued at $515k - $412k.  If the $412k included any fees/closing costs those would not count.  The gift is the fair-market-value of the house minus what your daughter paid to you.

Note that there is no actual gift-tax due until your total lifetime gifts exceed about $12 million. What happens is your From 709 gifts over $15k/$16k a year are totaled up when you die and added to everything you own at that time. If < $12 million there is no estate tax. The $12 million figure could change. It used to be $600k and is schedule to revert to $5.5M in 2026.