There is nothing unusual in a child of two and a half years being very attached to the mother. If he were not attached to the mother, one would worry!
Regarding the child's fear of you; perhaps because of a busy schedule, you do not have much time to spend with him. When you do have time, you want him to go out with you and play with you. It would be a good idea for you to read a story or tell a story when he is in bed and ready to sleep and let him see the gentle side of you. Do a funny drawing for him or a clay model or a paper boat. He has to know the playful father, before he has the confidence to go out with him! Do not force him to do something, so that he can be a big boy. There is time enough for him to grow up. Both parents can go out with the child. Please do not ask him if he likes the father more or the mother more. This question makes the child uneasy and it is not fair to ask him that.
Also, each child is unique and will have his own pace of development and his own preferences. As parents, we should be sensitive to the child's needs and
supportive of them. Enjoying your parenting will take care of most problems.