I was sent a penalty from IRS of 501.57$ for failure to pay proper estimated tax. Turbotax says I owed 15483, while they say I owe 15611.00

Is that "owed" the final tax, the estimated tax, or the penalty?  I can't follow your numbers.  Is the IRS saying the penalty calculation is wrong or that the tax calculation is wrong?

TT calculates an estimated underpayment penalty based on your entries in the program  however the feds & state reserve the right to access a final underpayment penalty, late filing penalty or late paying penalty ( plus interest ) based on the info they have and when the balance due was actually paid.     https://www.irs.gov/individuals/understanding-your-cp14-notice