Hello,
My answers
"
Correct me, So Now I can fill and get Birth Certificate in below form
1. Name of Child: Desired Name & Surname (Correct spelling)
2. Father’s Name: Existing Name & Surname as per his existing documents"
If you follow my last suggestion, you will find that I have suggested you enter your Son's name according to the expected spelling (for the Surname specifically). Birth Certificates do not get into the details of how the father's name is spelled unless that is Computerized and the digital form rejects the entry. First, try to input the correct Surname for yourself in his birth certificate and see if the corporation or municipality raises any questions.
If it does, you can do an affidavit for yourself as one and the same person and attach it with the certificate, though I believe that won't be required. If you have time you can do the affidavit before applying for your son's birth certificate and directly move with the process. So either way, it is advisable not to enter the unexpected spelling for his surname. Further, if your family or father's surname is spelled correctly and the way you want, it can be a good reference you can furnish before the concerned authority to establish the misspelling in your case.
All of these are because your current Surname, according to you, is not spelled correctly in your documents and eventually needs to be corrected. This way you are avoiding going through the same process for your son to correct back misspelled surname for him in the future and at least get his records straightened out from the beginning.
Your second question:
"
In this case there will be difference in Surname for Father & Child, but it will not create any problems while applying
Passport, VISA or any property transfers."
These days all documents start with Adhaar. So right after the birth certificate it is advisable to get the Adhaar card done for your son. Now,
I will advise before filling up his Adhaar form if not done already by then, you should definitely get your affidavit and have his Adhaar records with both your and his Surnames as expected.
Because, Adhaar will eventually be used to issue other documents like Passport etc, this will reduce hassles for you and your son in future.
Although, I have not seen Adhaar entry form to complain about different spellings for the father's name but because the Government of India is trying to centralize and maintain
all citizens' records to minimize ambiguity and duplicacy that often arises due to differently spelled names, my personal advise will be to do your affidavit and keep it handy for such
entries that may complain about different surnames and get the records entered correctly.
From here on, please ensure that the correct Surnames are entered in all his future documents to avoid chances of mismatch.
Please feel free to get back if you require further clarification.