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Japt, 8 bytes

ËùDV*EvV

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Explanation

 Ë ùDV*EvV
UmDE{DùDV*EvV} Ungolfed
 Implicit: U = s, V = n
UmDE{ } Replace each char D and (0-)index E in U by this function:
 EvV Take 1 if the index is divisible by V; 0 otherwise.
 V* Multiply this by V. This gives V for every Vth index; 0 for others.
 DùD Pad D with itself to this length. This gives V copies of D for every
 Vth index; 1 copy of D for others.
 Implicit: output last expression

I have to credit the idea to use ù to @Shaggy's answer here. I don't know that I ever would have thought of it myself...