In front of Presidio La Bahia is the Zaragoza Birthplace SHS.
From TPWD:
Ever wonder why we celebrate Cinco de Mayo? This day honors General Ignacio Zaragoza, who defeated the French at the Battle of Puebla in 1862. Visit his reconstructed birthplace adjacent to the Presidio to learn about this Texas-Mexican hero, born here in 1829. Descendants of the original town of La Bahía, the settlement that grew up around the Presidio, still live in the area today. Don’t miss the adjacent Zaragoza statue, donated by the citizens of Puebla, Mexico.
Access to this side building is limited. I recommend calling ahead to check for availability. The Presidio and birthplace of Zaragoza are not part of the State Park. There are additional fees to access both. Please plan accordingly.
Exploring Texas State Parks 
Historical study is available through guided interpretive tours; tour fees apply. The museum is currently closed for site improvements. The mission is closed on Christmas Day. Free tours are offered on weekends at 10 a.m. and 2 p.m. Check the calendar for upcoming events or contact the park for more information.