Who is responsible for sewer line that is pluged between house and main line?

Normally the home owner, While this may vary by country ( we are international site) and specific easements and agreements)
But the homeowner owns the sewer line from their home to the sewer main.

If the clog is on your land, it definitely is your problem. If it's under a sidewalk out street before it connects to the main line, check with your city or town.