I will be awarded my degree for the ongoing undergraduate course in 2020. When can i apply for LLM overseas? I want to apply for the academic year 2020-2021. When should I start the application process?

You can apply to many LLM programs if you are expected to graduate before the LLM starts.

As for when to apply, applications will open soon at many programs that start in fall 2020 (for instance at law schools in the US and the UK). Some law schools have already opened their admissions cycles for 2020.

Applying early is often better, as more scholarship money will be available in earlier rounds. But you should only apply if you're certain you're putting forth the strongest application (good recommendations, letters of intent, etc.)