Hello,

I presume you're doing a government job and want to explore other options after completion of BA, of course you will be able to apply for that, you're not the first one to do it, many people being currently employed in government sector also try for other jobs, what might happen in your case is you may need No Objection certificate from your employer, this also depends on  what the official notification states and you have to go accordingly, you can also appear for departmental exam, this is usually for promotion or higher posts recruitment,