It seems fairly clear that Merope Gaunt did not attend Hogwarts; what magic she was able to perform was probably taught to her by her father before he gave up on her entirely, believing her to be almost a Squib. (Compare this question by Slytherincess, as well as her entry on the Harry Potter wiki, which also speculates that she was home-schooled.)
Things are less clear-cut when it comes to her brother, Morfin. He certainly shows enough magic ability to make Tom Riddle Sr break out in hives, and also enough to bang Bob Ogden to the ground with yellowish goo squirting from his nose and later on fire hexes at him and make him run for the hills and call for Ministry backup. So he was presumably taught more magic, for a longer period of time, than Merope was.
But where was he taught?
According to his wiki article, he was born some time between 1900 and 1907, so he would have been of schooling age from around 1911–1918 until 1918–1925. We know that Phineas Nigellus Black died in 1925 and was Headmaster of Hogwarts until his death, so it’s at least likely that Black was already Headmaster at the point when Morfin reached schooling age.
We need hardly doubt that Marvolo would not dream of sending his son to a Hogwarts led by Albus Dumbledore or—presumably—Armando Dippet; but Black, who shared Marvolo and Morfin’s views on Muggles and pure-blood supremacy, would probably be a different story.1
Is there any canon evidence whether Marvolo sent Morfin off to Hogwarts or home-schooled him?
1 Assuming Hogwarts, even under the Headmastership of Phineas Black, would have him, that is—Black may have been quite a nasty piece of work in many ways, and the most unpopular Headmaster Hogwarts ever had, but even he may have balked at the prospect of letting someone as obviously mentally unhinged and sadistically, psychopathically violent as Morfin Gaunt enter the school. Even an unpopular Headmaster presumably doesn’t want students murdering each other left, right, and centre.