Well, it depends on the context. Let me present two situations.

IN = inside

ON = Place something above another so that the former touches the latter.

Situation 1: ‘IN’

Since investment (money) is not placed above a product but inside it, investment is never ON but IN. You invest inside a company, inside gold, inside a business (become a part of them).

Correct: invest in something.

Situation 2: ‘ON’

ON = used to refer to a position/ process. (the house is on fire)

So, when you follow a process before investing, it uses ON.

I invest on the basis of Warren Buffet’s advice.