How does a narcissistic husband explain his infidelity and the fact he has children with his mistress if after being caught he admitted to adultery but denies having children with his mistress?

The narcissistic has deep unmet needs for affirmation from the outside because deep down they don't feel good about themselves. Oftentimes this causes complications in their everyay life and relationships, and like any fix it is only temporary. Denying parental responsibility is not limited to narcissists. He could be asked or in some circumstances may be required to have a genetic test to determine whether or not he is the father.