Easy way out to do private online job along with govt job

Even an online job also can't be taken up by government employees. If it is for an hour or two after the office hours and working in sites ISC where it is not treated as a job can be OK. But you should show that income also likes your income and pay tax.

But you are telling it is an online job. What are the working hours? Are the time matches in both the jobs? If the working hours are the same at any point in time you can't work. If the timings are different you can get the job on the name of any other member of your families like your wife, son or daughter and you can work. But the money should go into the account of that member-only but not on your name.

Any amount reaching your bank is accountable, if your income is falling in the tax bracket.
It is good to have an online job wherein the income is meagre just to get knowledge and support your spare time.
If you really want to make more money, you have spend some time regularly as well as eventually to gain the expected incomes.

Strictly speaking Govt servants are not allowed to do part time jobs and whenever Govt requires Govt servants for the additional or some occasional duty like election duty, they can be called to report failing which disciplinary and administrative action would be taken against them. So from that angle it is not possible to do any such assignment online even on the different hours. However people associate with some family member or friends who are working in a private place and in their names many people engage themselves in online jobs to earn a little extra income. So, one has to be particularly careful in this respect and should not do anything against the rules and regulations.

While engaging oneself in any job even part time in nature, the government servant should go through the model standing order. As far as I know being a government servant, you are not supposed to take up any job, volunteerly or otherwise without taking the consent of your personnel department.
If your appointment letter is indicating that you should not undertake any job getting some remuneration or otherwise, you need to follow such a rule otherwise you will invite yourself for the displinary action.
The philosophy behind this rule is that any engagement apart from your present central government job can divert your mind from the assignments to be discharged in the central government job.