Produce n n-squares of integers with rotating *'s in consecuitive corners
Dyalog APL, 57  bytes

Requires ⎕IO←0 which is default on many systems.
Assuming double-spacing is permitted, as per the OP's first example.
{A←⊃∘⍕¨?10⍴⍨3⍴⍵⋄A[(⍳⍵),¨⍵⍴2↑¨1⍵(⍵ ⍵)(1⍵)-1]←'*'⋄⍉⎕FMT A}

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Non-competing 49-byte solution (Dyalog APL 16.0):
{⍉⎕FMT'*'@((⍳⍵),¨⍵⍴2↑¨1⍵(⍵ ⍵)(1⍵)-1)⊃∘⍕¨?10⍴⍨3⍴⍵}