How to restart a process using the Web API

 [mention:09def98cea664ff8b2b1b4e8d229ac58:e9ed411860ed4f2ba0265705b8793d05] I have not come across the scenario you have described,  we can pause the process model by 2 ways, 
1. using Timer smart service, here process will halt for duration of time you have mentioned,
2. Using Rule smart service, here process will wait based on the logic you design, for more info docs.appian.com/.../Rule_Event.html

You can try the Process Management plugin to achieve this.

community.appian.com/.../process-management-services

community.appian.com/.../kb-1340-how-to-automate-the-restart-of-stuck-nodes-within-a-process-model

For what purpose? IMHO this is not something you would do in Appian.

Maybe this helps: https://appian.rocks/2023/03/20/design-long-running-tasks/