I work on linux server and I don't kwon nothing on mainframe.
I suspect you could use cron on the linux server. . . You need to talk with someone who knows your mainframe - what is available on that system is quite site-specific.
NO scheduling soware is actually used. If you can suggest one is good.
Why do you believe this if you know nothing about the mainframe? It may be that scheduling software has been installed, but is not properly used. We (the forum) try to help with technical questions. We don't make product recommendations.
If your mainframe truly has no scheduling software and it has been decided that such software is needed, your management will have to decide which to install. I've supported more than 100 mainframes in recent years and 100% have scheduling software installed and in use. Indeed, they would not survive a day without it. . . .