I want to ask, is ziarat ashura and waritha something I should recite every day? I was not sure if they were just if I went to visit Karbala. Also, what are recommended things to say after prayer besides tasbih Fatima (a.s.)?

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You can recite the shorter one ziyarat warith. It is not obligatory. If you couldn’t do it you don’t have to. It’s good to send salaams to the prophet and the 12 imams everyday. It can be a short salaam or the long ziyara. After tasbeeh zahra there are daily supplications after each prayer. You can find them on duas.org

It is also recommended to recite Aytul Kursi after each prayer 2:255