I cordially welcome you to the Moodle forum. It’s a nice idea to share each other’s problems which eventually ends up in a learning process.
As far as I’ve understood; you wish to show your assignments to a particular group of students who can view and attempt that particular assignment; but it's not happening in actual. I’d like to tell you that you’ve to do this with groups in Moodle. Suppose there are two groups, group-A and group-B, and you want to make the assignment visible to only group-A, then assign the group-A to that particular assignment.
There’s a link given below for further reference:
We’re happy to offer help to any fellow Moodler. I wish you a smooth path ahead. Please feel free to get back to us for any further query.