How to create a self signed certificate for authen

Question

This question already has an answer here:

• How to create a self-signed certificate using C#? 5 answers
• Generate and Sign Certificate Request using pure .net Framework 1 answer

Background:

We have to implement a custom authentication mechanism for identifying and authenticate my client's applications and initial details can be found here.

Finally, We have come up with the conclusion that we will simply use self-signed certificate for encryption and decryption of JWT token.

Now I'm figuring out the answers of following questions:

Are there any dotnet libraries available for creating self-singned certificate or I should write my own code for the same?

If I would be issuing a self-singned certificate to my different clients for the secure authentication and communication then how that certificate would be updated at client machine after an expiry?

Edit:

The client needs to sing JWT token using the issued certificate before sending it back to my application.