According to USCG, the search was suspended at around 7:55 a.m. on Sunday.
At around 11:20 a.m. on Saturday, crews received a call reporting that the father and son were overdue.
The pair had reportedly departed at 5 a.m. to shrimp off Magnolia Beach in a shrimping vessel called 'My Possum,' and were due to return at around 10:30 a.m.
Watchstanders issued an urgent marine information broadcast and directed the launch of a helicopter crew from Coast Guard Air Station Corpus Christi and a 29-foot response boat from Coast Guard Station Port O'Connor.
A fireboat crew from Calhoun County arrived at the scene and reported a capsized vessel matching the 'My Possum' description in the Matagorda Ship Channel off Magnolia Beach.
"Unfortunately, after considering all pertinent factors, we made the difficult decision to suspend our search today," Homar Barrera, search and rescue mission coordinator with Sector Corpus Christi, said.
Anyone with information is encouraged to contact Sector Corpus Christi at 361-939-0450.
EDITOR'S NOTE: The Coast Guard had previously been informed that the missing man was 35 years old. The missing man is 50 years old.