Here's the breakdown:
* Timmons's is the possessive form of the singular noun "Timmons". It's used to show possession, like "Timmons's house" or "Timmons's car".
* Timmonses' is the possessive form of the plural noun "Timmonses". It's used to show possession for multiple people named Timmons, like "the Timmonses' family reunion" or "the Timmonses' business".
Without more context, it's impossible to say for sure which form was intended. If you can provide more information about how the word was used, I may be able to give you a more specific answer.