When writing in a academic setting (think of a letter to your professor), what is the most appropriate way of saying this?
I will be grateful if you could resolve this doubt in your paper.
I will be grateful if you could dispel this doubt I have in you paper.
You can suggest better alternatives than those in the title.
Neither is correct in American English. As we use it, “doubt” is not a synonym of “question”, and would never be used in these sentences. It generally implies a challenge to a statement, rather than an uncertainty. Both “resolve” and “dispel” could also be read as possibly implying a challenge in this context, since they imply that the problem is in the paper rather than in your understanding of it.
I think what you are trying to say is “I would be grateful if you could answer a question I have about your paper.” (Also note the use of “would”, to match “could”, and “about” rather than “in”.)