AL SHIHR, Yemen — When fighters from Al Qaeda seized control of a stretch of southern Yemen in 2015, they looted millions of dollars from the central bank, spreading such fear that other banks shut down.

But during the year Al Qaeda reigned, Al Omgy Brothers Money Exchange kept running its business here in the coastal town of Al Shihr. It held accounts for the national oil company, disbursed salaries for the Yemeni government and earned the praise of local officials for providing needed services during a tough time.

And if members of Al Qaeda wanted to open accounts, too, well, the company could not really say no, according to Muhammad al-Omgy, who runs the money exchange with his brother, Said.

The United States was not impressed.

This month, the United States Treasury Department designated the brothers and their company as having provided “financial services to or in support of” Al Qaeda in the Arabian Peninsula, which is widely considered to be the terrorist group’s most dangerous branch. Any of their assets subject to United States jurisdiction are blocked, and Americans are generally prohibited from having transactions with them.