Key Check Value standard practice for asymmetric cryptography?
PKCS10 looks like relevant industry practice for private keys.

See "Note 2" at page 4,
Certification Request Syntax Specification - RFC 2986:
The signature on the certification request prevents an entity from requesting a certificate with another party's public key.

That is, soneone requesting a certificate on a public key demonstrates his knowledge of corresponding private key by producing a signature verifiable with the public key from PKCS10 request.

Another technique could be found at Join protocol,
Direct Anonymous Attestation
for Trusted Platform Module chip.
It could be considered a proof that TPM "has access" to "keys" $f_0$ and $f_1$.