have (one's) doubts (about someone or something)
To be wary or uncertain of someone or something. I know you really love this neighborhood, but I have my doubts. I do have my doubts about Brian—he just seems untrustworthy to me.
have doubts about someone or something
to have questions or suspicions about someone or something. I have doubts about Alice and whether she can do it. We have no doubts about the usefulness of this project.