From Business: First Community Bank is a regional retail bank that serves residents and businesses in the Corpus Christi, Texas, area. It offers a variety of. The latest Tweets from First Community Bank (@FCBofTexas). Locally owned and operated in South Texas, we are a Community Bank working to help the Communities we serve. We are hiring for a Teller Supervisor in Rockport, TX. First Community Bank (TX) is headquartered in Corpus Christi and is the th largest bank in the state of Texas. It is also the 1,th largest bank in the nation.