Hello aspirant,
I am here for helping you....
yes you definitely can apply for government job after 12th class there are several government job opportunity which you can have after completing your class 12th so I am providing you list of these government jobs.
Forest Guards

Ticket Checker

Indian Army

Railway Clerks and Constables

SSC Stenographer (Grade C and D)

Delhi Police

BSNL Direct Selling Agents (DSAs)

I hope it will be beneficial for you....
For more queries you can  upvote my answer and can ask in the comment section below...

Best of luck...