Awwww....what a cute widdle kitten!
Hybrid Big Cats
Hybrid animals almost certainly only exist in captivity and are the result of human intervention, along with the unnatural living circumstances presented by captivity, and on occasion, artificial insemination. Small wild cat and domestic cat hybrids have been introduced as pets, but those species are usually several generations removed from their wild ancestor.

Pumapard. Offspring of a puma and leopardess.

Servicals. Offspring of a male serval and a female caracal. The offspring of a male caracal and female servals are called caravals.

Tigon. A cross between a male tiger and female lion.

Liger. A cross between a female lion and a male tiger.

Leopon. Cross between a leopard and lioness.

Jaglion. A cross between a jaguar and a lion.

Bobcat-Lynx hybrid.
It is extremely unlikely that such hybrids occur naturally.
Likely encounter of two different wild cat species in the wild:

Lion:Hey stripey, what the hell do you think you're doing in my territory?!
Tiger: Me?! what the hell do
you you're doing in my territory, blondie?!
Lion: ROAR!
Tiger: ROAR!
*fur and fangs fly*