Regular study with government job

It all depends on your relations with superiors.  Normally, if you are in employment and wanted to attend classes, you have to obtain written permission for such study assuring them that your work will not be neglected and that you can not state the reason for stoppage of a routine transfer for such education.  Infact, the more qualified the employee, the more convenient for the employer.

First, stop worrying as you have not resorted to criminal offense and in no way neglected your job and concealed any disqualification for getting such employment.

Do not neglect your job and maintain good working relations so that they may encourage you for your career growth.

Depending on such employment notification, you may have to obtain prior permission for applying through proper channel and should not conceal present employment while applying for other jobs.

Where you are employed - with the Central or State Government? Has the leave,  as applied, has been sanctioned? 

Any how, there is no service law which lays for any special conditions or restrictions for sanctioning leave for study purposes or appearing in examinations thereto. However, the general principle is that employee cannot claim leave as a matter of right and it is  open to the leave sanctioning authority to leave at its discretion. Thus, continuing study or appearing for examination is not a ground for the emplyee to remain absent from duty unauthorisedly.

Whatever the case, once you complete graduation, you can apply for other jobs based on that qualification. It is only that you need to apply through proper channel. If you are a Central Government employee, it is sufficient that due intimation is given to the Controlling Authority/Head of the Office while applying for recruitements through UPSC/PSC/SSC.