X.509 Section 9.8.3.
This extension may be used as a public-key certificate extension, a CRL extension or an AVL extension. It shall contain the algorithm identifier for the alternative digital signature algorithm used by the signer when creating an alternative digital signature and by the relying party when validating the alternative digital signature.

altSignatureAlgorithm EXTENSION ::= {
    SYNTAX AltSignatureAlgorithm
    IDENTIFIED BY id-ce-altSignatureAlgorithm }

AltSignatureAlgorithm ::= AlgorithmIdentifier{{SupportedAlgorithms}}

When the altSignatureAlgorithm extension is included in a particular value that is an instance of a data type that supports extensions, the altSignatureValue extension shall also be included.
NOTE 1 – By having a separate altSignatureAlgorithm extension, instead of having it combined with the altSignatureValue extension, the alternative digital signature algorithm is protected by the alternative signature. This extension may be flagged either as critical or as non-critical.
NOTE 2 – It is recommended that it be flagged as non-critical. Flagging it as critical would require all relying parties to understand the extension and the alternative public-key algorithms