It sounds as though there may be "steps" involved here, meaning stepfather, stepmother, etc. If your mother and her "sister" are not blood-related sisters, meaning that they either did not have the same father or mother, then they are either half-sisters or stepsisters. Even if that's the case, you and the daughter of your mother's "sister" would still be cousins, even if that means you are "stepcousins" or something similar.
A good example of this might be found in a family where either the mother or father re-married: If the father re-marries, you would now have a stepmother. If the mother re-marries, you would then have a stepfather. In either case, offspring produced by your stepbrothers or stepsisters (or half-brothers/half-sisters) would be considered "stepcousins" or perhaps even "half-cousins" to your own children. Hope this helps.
A daughter (or a son) of your mother's sister (or brother) makes you cousins. If she's the child of your mother's (or father's) brother, that still makes you cousins.
Many riddles or "messy" problems begin with an apparent conundrum and they intentionally mislead the reader by the way they are phrased. Solving a riddle routinely requires original thought and resourcefulness although the answers are often almost ridiculously simple with hindsight. This question poses a simplistic riddle. Problem-solving techniques help to solve riddles as analytical skills are needed. The reader or problem-solver must look beyond any unnecessary detail by analyzing information in order to solve the problem. The idea is to search for key information and to break questions into smaller parts. In problem-solving, the difficulty lies in trying to find the overall answer without taking time to consider each step. Each step has to be considered on its own merit and as part of the whole.
To consider the relationship described in the question requires breaking the question down into elements. First find the potential answers to the each part.
1. My mother's sister would be my aunt.
2. The daughter of my mother's sister would be my mother's niece.
3. This would make me and the daughter of my mother's sister cousins.
4. My gender, male or female has no bearing on the question.
However, the question has another element. If my mother is not "directly" relater to her mother and yet they are sisters, the reader has to decide if this is relevant to the question and if it will in fact change the answer at all or if the information, upon analysis is unnecessary for the purposes of finding the answer.
There is a need therefore to understand "directly."
1. It could mean that the are not biologically-related. The reader can deduce that this will not change the answer as the statement has been made that they are nonetheless sisters.
2. It could mean that they are step-sisters and so have no biological connection. Again, the answer remains the same. Interestingly, this answer could change if there were any marriages within step-families.
3. It could be that the term sister is used for sister-in-law. This means that either the "sister" is my father's sister (and so my mother's sister-in-law) so the answer remains the same because the daughter is my father's niece in this case anyway. It could be my mother's brother's wife which makes her my uncle's wife which means the answer still remains the same.
The answer to this riddle is, as aforesaid, that we are cousins.