You're not wrong. Both of those sentences are correct. In the first sentence, you are considering your doubts separately. Maybe you have several different doubts relating to a particular issue. The opposite of this is 'I have no doubts.' In the second sentence, the word 'doubt' is an uncountable noun. It refers, in a more general sense, to the abstract concept of 'doubt', or lack of certainty. Another way of saying this is 'There isn't any doubt' and the opposite is 'There is some doubt'. If ever you see a singular noun used with the words 'some' or 'any', you know that it's an uncountable noun (like 'some/any money' or some/any water') There are other words with similar meanings that work in the same way. For example, you can either say 'There are some concerns' (plural) if you are considering these issues individually, or 'There is some concern' (uncountable) if you are referring more generally to a feeling of concern. Other examples are 'difficulty' and 'question', which can also be either countable (singular/plural) or uncountable (singular only).

Well,Hamed, you certainly ask difficult questions. In the positive, I have doubts is in the plural because the person has many/ several doubts. However, in the negative he has no doubts but we use a noun phrase "no doubt" ,which is really a shortened version of " not a single doubt" to emphasize the fact that he is sure.I think this is right, but your question is a very tricky one, so others may disagree.Let's hope someone else pitches in here!