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Transit visas are not applicable to you (you would need a permanent resident visa in a bordering country (other than Qatar) to apply for a transit visa), there are also no visas on arrival for Saudi Arabia.
Your only option therefore is to apply for a family visit visa (your father can request it on your behalf). Once approved, approach the embassy to have it stamped on your passport.
It will be a single entry visa valid for 90 days.