Are you saying that your mom and uncle are stepbrother and stepsister? In other words, they are from the same dad but he had subsequent marriages?
That would make you and your cousin half first cousins, or stepcousins I guess. There is often a prohibition in a society against first cousins marrying, but possibly the fact that you are not as genetically connected as you would be if your mom and uncle were brother and sister would ease that prohibition.
If the law doesn't prohibit it, and if your family has no genetic issue that travels down the male line that you would be concerned about, it doesn't seem like you would have a lot of problems. You might consult a geneticist.
If I got this correct, your mother and her brother (your uncle) are half siblings (same father but different mothers). That would make your uncle's daughter your half first cousin. The children of first-cousin marriages have an increased risk of genetic disorders though some scientists/researchers believe the risk is relatively small. I am not sure if the risk decreases in your situation though.
I've noticed that this is a culteral thing-------- quite taboo to marry family in the US but rather common in other parts of the world. What is the culteral norm about such unions in your country? If it is not common and frowned upon, that makes things much harder.
Otherwise, as Londres said, speak to your doctor about any ramifications if you produce children together-------- possible ones I should say. What types of genetic issues could occur and how likely they are. good luck
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