I don't have a group yet

"I don't have any group member yet." is incorrect. If you wanted to indicate that you have a group, and are seeking members, but haven't yet gotten any, you would say "I don't have any group members yet."

"Can i fill you group?" is a rather awkward sentence. It implies that you could find a sufficient number of people willing to join the group to meet its membership goal. If you mean simply that you wish to be a part of the group, you would say: "Can i join your group?"

WB: -I don't have any group member yet.
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-I don't have any group memberSHIP yet.

-I don't belong to any group yet.

Thank you~~