Digital Ocean is probably the best known "cheap" hosting provider.
Using ASP.net almost certainly means you need to use a Windows server and those are always going to be more expensive then linux servers due to licensing.
AWS does have free tiers for Windows so that'll give you a cheap way to start a project.

Look for Free tier eligible in the Choose an AMI after clicking Launch new instance.
Personally if I was going to run Windows servers; I'd run on Azure. What better hosting company for a windows backend then from the company that makes it? Information about their free tier can be found here