Your chances are extraordinarily small, of confirming any connection through DNA. There are 3 types of DNA tests, autosomal, yDNA, and mtDNA. Autosomal tests (Ancestry, Family finder, etc) are only useful up to about 6 generations away, very rarely a seventh generation, so it's out. yDNA is strictly a male line thing, so all you can prove is a connection from Jerome Svajda to a proven male relative of hers. I don't think there are any proven male relatives, so I'm rather sure that's out too. That leaves only mtDNA, but it's strictly passed down through mothers to daughters, no males at all. Matthew does have the mtDNA of his mother Catrerine and grandmother Josie, so if your Indian connection could be through them, then it's remotely possible to find a suggestive DNA connection. But if they don't have Indian blood, then it's not possible to find it through anyone else, not with today's technology. To get that mtDNA test result, either Matthew or his mother could be tested, a mitochondrial DNA test.
The next problem is that to test a connection, you need tests of 2 different and distant descendants, for a comparison, at least one of which has a proven paper trail documenting their ancestry to Cleopatra. And at that distance of 12 generations, most DNA veterans would say you need 3 matches to confirm, not just one other match. That's not impossible, but going to be very difficult, many obstacles to overcome.
