Can Convict cichlid Live With Oscar?

This one cuts both ways. A convict cichlid's reputation is not exaggerated: it takes on fish several times its own length and regularly wins on attitude alone, so a 35 cm oscar sharing its space should expect to be harassed rather than deferred to. The oscar's side of the risk is size: its own profile says its predatory nature rules out much smaller fish, and a 15 cm convict is well under half its length once the oscar is grown.

24 to 28 °C and pH 6 to 7.5 suit both, so water is not what decides this.

If you try it, raise both from a similar starting size rather than dropping a small convict in with an adult oscar, and use the oscar's own large tank, 540 litres or more, so the convict has territory to hold that is not directly contested. A convict that will not stop harassing a much bigger tankmate, or an oscar that starts treating the convict as food, both mean the same thing: move one of them out.