How to apply for visa if father's documents are from another country?

There are two issues. One is your father's documents are from a different country. The second issue is the surname of your father is different in your documents.
There will not be any problem for you to get VISA to study abroad even though your father's documents are from a different country. You will not face any issues.
But the income certificates that you are going to submit for your VISA should contain the same name as your father's name in your Passport. There should not be any different. If any difference is there your VISA will not be processed. So you have to apply for a reissue of your passport with the correct name of your father.
You can refer to https://passportindia.gov.in/ to get all the details regarding the papers that are to be submitted for a change of your father's name while applying for the reissue of the passport.
Otherwise, you can take the help of a local advocate and get an affidavit made in which you can mention the name of your father correctly. After making the affidavit, you have to publish the same in two newspapers about the change of father's name. One in a local language paper and the second one in an English newspaper and then you have to apply for a gazette publication. You can get the full information from the advocate.

It will be difficult for you to get a visa in your favour unless all this certificates and his name entered in the different documents are identical in all respects.
While making visa in your name, you need to ensure the uniformity of all his certificates and wherever your father's name is reflected in your certificates, their should not be any mismatch. While his income certificate would be essential for you to be produced before the Visa Officials so that your Visa could be processed successfully in favour of your name, you need to ensure correctness of the relevant documents.
There should not be any any deviation in respect of names between your passport reflecting his name and the visa which is to be processed.
Though officially, it will take time to reissue your passport free from errors, but there is no other way.
The alternative way is to make an affidavit indicating that his name as shown in his income certificate in respect of his surname and other documents ate not the two persons but are the same. Your appointed lawyer will help you in the process of affidavit and once the affidavit has been countersigned by the first class magistrate, get the same published in the local newspaper apart from the leading English Newspapers for the wide publicity.
One xerox copy needs to be produced to Visa Officials for getting your Visa processed.