The provider plugin protocol changed in Terraform 0.12 to support the various new features in that release. You must therefore build a new version of your custom provider to use it with Terraform v0.12.0 or later.
The Terraform SDK team wrote a guide to upgrading existing providers for Terraform v0.12 compatibility, which should be sufficient to make your provider work correctly with Terraform v0.11, v0.12, and v0.13.
That guide also includes a note about switching to the standalone SDK after you’ve completed your initial upgrade, but I notice that the link in the text is incorrect at the time of writing. The guide it intends to link to is Switching to the standalone SDK. That’s optional if you don’t intend to do any further development of your provider that might benefit from newer SDK features, but since there is an automatic migration step for this (once you’ve completed the initial upgrade in the first guide) it may be worth just trying it anyway.
Please note also that the end-user-oriented upgrade guide for Terraform 0.13 assumes that you have completed an upgrade to 0.12 first. If you try to move directly from Terraform 0.11 to 0.13 then you might encounter problems that the upgrade guides don’t anticipate.