I want to get specific publication list for specific User (depending on those user group's rights and permission in which that user is associated with). I tried with PublicationData class or PublicationFilterData class and I am getting all available publications but I want specific publication list based on user.
You could impersonate that specific user in your code and then request all publications as them. This should give you the complete list that they're able to access.
Alternatively, you could get every publication and then iterate over them to determine whether the user (or a group that they're a member of) has any rights on that publication.