If you own your home on January 1st, you can file a Homestead Exemption on your property!
Texas is a non-disclosure state so no one knows what you paid for your property. When you go to the Appraisal office to file your exemption, there will be a blank asking what you paid. You DO NOT have to fill that in, UNLESS the amount you paid is LESS than what they have your property appraised at.
If you get stuff in the mail wanting you to pay to file your homestead exemption, THROW IT IN THE TRASH! Filing your homestead exemption is FREE!