Will my father's Florida's homestead tax credit be affected if he decides to add his children, who resides in NYC, to the deed of the home?

You will want to contact the Property Appraiser for the county in which he resides and claims Homestead Exemption. If it is in Osceola County, you may contact the Office of Katrina S. Scarborough (407) 742-5000 or via the website www.property-appraiser.org

Not sure speak to an Estate Attorney, I recommend Lee Massey in Saint Cloud, FL or find one near where he lives