JavaScript (Node.js), 60 bytes

Expects (permutation_string)(string).

p=>s=>(B=Buffer)(s).map(c=>(B(p)[q=c&32,c-q-65]||c)&95|q)+''

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JavaScript (Node.js), 60 bytes

Expects (permutation_string)(string).

p=>s=>(B=Buffer)(s).map(c=>(B(p)[q=c&32,c-q-65]||c)&95|q)+''

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JavaScript (ES6), 42 bytes

Assuming using lists of ASCII codes is acceptable:

p=>s=>s.map(c=>(p[q=c&32,c-q-65]||c)&95|q)

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