A foreign child will attend a private school in Bangkok, guess the minor will be entitled to a student visa, as the child can not be left alone and need to be cared, shall be the mother allowed to obtain a visa and if positive what kind of visa she shall apply ? 
thanks

The child would first need a non-ed visa and then apply for an extension of stay at immigration with supporting documents. Most schools will know what is needed if there are other foreign students attending the school.

The mother would need a non-o visa and then she could apply for an extension for being their parent. She would need 500k baht in a Thai bank for 30 days when doing the first application and then 90 days after that.

See #5 heere. https://www.immigration.go.th/content/service_11