how to schedule jobs using script

You can schedule daily, hourly, by minute, continuously, or even incremental minutes. The incremental minutes is a little hidden...I’ll give you that. But, it’s possible to do many different types of schedules.

Well, that’s how Veeam, or any backup product works. Not sure any product can do exactly that type of schedule. For Veeam, you utilize both the Backup Type (Forward, Forever Fwd, Reverse) and Retention (configured restore points or days) to decide on when a Full vs Incremental gets created. Then additionally, yes, you can add an extra Full to break up your chain. I think you can partly do this by configuring a Fwd backup, selecting to either use Synthetic or Active Fulls (your choice based off your need) & configure it for ‘Monthly’ and ‘On this day’ and select 15. I think the only way to achieve adding a Full on those 2 days per month is create your backups to start on the 1st; set a 30 day retention, then configure your additional Full as I just shared. It still wouldn’t do exactly as you want because there are obviously months with 30 days, 31 days, and (mostly) 29 days. I’m not sure of any script, etc. to do a schedule like you’re wanting. At the very least you could ping Veeam Support to see if there is a way → a Registry change, for example?

Powershell is probably where you’re going to want to go on this.  The PowerCLI can run jobs a little differently I believe if that’s what you’re looking for and then as noted above, once you get your command as you want, you should be able to set some task scheduler events to kick off each command as needed.  The way you want to run backups are a bit niche, but if you think it’s something that others would see value in, can’t promise anything here, but you could post a feature request in the R&D Forums.