New Closet Rod

Hi, ok I know I am doing something wrong. I am relocating my closet rods much higher so I can put a lower bar in there too. I keep scanning my walls with the Zircon stud finder (not the cheaper one the one that does deepscan, metal scan, ac scan also).

Anyways it lights up a beam for me and it seems the screws I have (i used replacements screws instead of the ones that come with things) went in easily. On top of that they continuously turn, they never tighten. Out of the 4 screw holes one of them tightened. I took them all out and was going to anchor them. As of right now all the holes I made I just patched up so I can attempt again in a new location.

What is the best way I can get a closet rod sturdy. Should I keep trying for a beam or just use the anchors? If the screw doesnt stop turning and never tightens I assume I am not in a beam? Any help would be appreciated, thanks!