How to change the spelling in income certificate?

Where from you obtained the income certificate of your father? Who issued the same? Did you give the proof to him about your father's name?
To get the income certificate you have to approach the person who issued that. You have to explain to him the mistake in the name in that certificate. You have to show him an identity card of your father in which his name is correctly spelt. You have to tell him that the correction is needed on the same certificate. If he gets satisfied that there is a mistake in the certificate, in the same certiifcate he will change the spelling and put his signature there and he will put his stamp also. This will solve your problem.

For the correction of father's name in income certificate, you must approach to the Department from where the certificate was issued.
If the certificate was issued online, then fill application for correction in name online with ID proof.
If it was issued offline, then you will have to submit an request application for correction in name spellings along with Identity proof or document having correct name of your Father.
Their might be some fee for correction in name, you will also have to submit the fee.

Income certificates are issued online as well as offline. You have not given enough information. Where did you get your income certificate? Did you apply for it online or offline?

This certificate is issued by the revenue department of Indian states. Visit the department from where you collected your income certificate. Carry all those documents which you submitted as proofs. You can register a complaint there. Fill out a new form and make necessary changes in the spelling. Submit the form to the concerned authority. The needful will be done at the earliest.

It is not a big thing. You can approach I the authority who issued the certicate with a proof in original which has name with correct spelling. Aadhaar/voter id/pan card is considered as good proof. Approaching the authority in person is advised.

As income certificates are issued by local village office(or any other equivalent office as relevant), it is always easy to approach them and get the needed correction on the certificate. Many times the spelling changes happen when the names are written from native language to English or vice versa. The issuing authority can very well understand that and they can make necessary corrections.
However you may also carry a suitable proof to make things easier.

If it is a mistake then it should be corrected at the issuing place by the authorities from where it has been issued. There is simple procedure for correction and you have to apply for it giving the details. Please note that error could have been resulted due to many factors and we can not blame them always for it. Anyway, when you go for the name correction, you have to keep some original valid documents so that the authorities can cross check it for the credentials of the person. Once that is confirmed then they will issue the corrected certificate immediately. There could be some little fee also for that.