TLDR: They will kill unrelated kittens, and may not be able to tell the difference.
Females usually do not allow the male to approach the kittens as
he may kill them because he does not recognize them as his own offspring. When a resident male is killed and a new male arrives in the vacant territory, he may kill all the kittens that he finds because they are not his offspring and because once the young are destroyed, the female will be more likely to breed again, producing
Adult male cougars do not participate in kitten rearing. Indeed, adult males sometimes kill kittens when they encounter them, a behaviour that may be part of the male cougar reproductive strategy. Killing kittens sired by unrelated males can increase the reproductive success of the infanticidal male by providing an opportunity to breed with the female sooner
Causes of kitten mortality have been less well studied. In populations where kittens were
monitored, most deaths are a result of natural causes such as starvation or infanticide by males
(Logan and Sweanor 2001, Cooley et al. 2009). In most North American states and provinces,
including Alberta, hunters are not permitted to shoot spotted kittens or females cougars travelling
with spotted kittens
Management Plan for Cougars in Alberta Wildlife Management Planning Series
Breeding males and females spend only a short time together after which time they separate, with the male playing no role in the rearing of young.
Kittens (also called cubs) weigh just over a pound at birth. Until they are two weeks old the kitten’s eyes and ears are closed. Kittens have blackish-brown spotted coats, which serve as camouflage to help conceal them from other predators, including adult male cougars.
Cougar Reproduction and Maturation
The advantage as states above is that by killing unrelated kittens, the males have a better chance of passing on their own genes.