which exponent to be used for RSA e =3 or 65537 for RSASSAPSS signature verification
Use the value of public exponent $e$ that came with the public key, here $e=3$ according to the question. Otherwise, signatures won't check.

Common RSA public exponents include $65537$ and $3$, and more generally the Fermat primes $2^{(2^k)}+1$ with $0\le k\le4$; and $37$ (used by Putty).

$e=3$ leads to the fastest RSA public key operation, because we can compute $x^3\bmod n$ as $((x\times x\bmod n)\times x\bmod n)$; more generally, when using $e=2^{(2^k)}+1$, the public key operation $x\to x^e\bmod n$ requires $2^k$ modular squarings and one modular multiplication.

Using $e=3$ is believed safe when used with good padding techniques (including signature per RSASSA-PSS as in the question), but $e=65537$ is recommended by many authorities and can sometime act as an effective patch (for example, it has the potential to save implementations of PKCS#1 v1.5 decryption from disaster by side channel leakage thru error codes or timing attacks; and faulty implementations of PKCS#1 v1.5 signature verification that incorrectly validate the padding).