I have a non O visa with a 1 year extension with my dependent son. Am I able to get a work permit with this visa?

Is your son Thai. If yes you can apply for a work permit and work.

If yes then you have a extension of stay based upon being the parent of a Thai.

Yes my son is Thai. I am also married to a Thai. For the first time I got a 1 year extension through an agent. I asked for a marriage visa but somehow ended up with a dependent child visa. 

A dependent non-o visa or extension of stay does not exist. You have a extension of stay based upon being the parent of a Thai.

Since you are married you would need provide a copy of your marriage certificate when the work permit application is done along with all the other supporting documents.

Understood. 

59 minutes ago, Possumdog said:

I asked for a marriage visa but somehow ended up with a dependent child visa. 

They give you this as it is better(no need to keep money in the bank). If marriage ext., you must keep 400k in for a couple of months.