Your presence not necessary you can appoint any advocate also to file the same on your behalf 

execute POA in favour of family member to do the needful 

2) POA should be attested before Indian consulate 

1. File the I‑130 now.

   • Attach a one‑page notarized affidavit from you, your wife, and (ideally) her father saying the father’s middle name is misspelled on the marriage certificate and giving the correct spelling.

   • Add a copy of the father‑in‑law’s passport (or other ID) that shows the right name.

2. Start the correction in India.

   • Give your wife (or a relative) a Special Power of Attorney, notarized and apostilled in the U‑S.

   • They file a “clerical‑error rectification” request at the same Sub‑Registrar with the certificate, ID proof, and the affidavit.

3. If USCIS asks for proof later (an RFE), send the rectification receipt and the same affidavit/ID again.

   • A parent‑name typo is routine; it won’t sink the petition as long as the spouses’ names match.

That’s it—petition now, fix the typo in parallel, and be ready to show you’re doing so.

Contact Indian Embassy/Consulate for help. In every Embassy there is marriage officer, you can get the correction done through him. 

Give a notary affidavit/undertaking before all/any Authority which raise this defect and question it.

To correct a misspelling of a father's middle name on a marriage registration, the first step is to contact the registrar's office or the department responsible for marriage registrations in your state. 

You will likely need to submit an application for correction along with supporting documents, such as an affidavit from the father stating the correct spelling of his middle name. 

It's also helpful to have copies of other relevant documents, like birth certificates or other identification, to support the correction.

To rectify the error online,  you may locate the official website for marriage registration in your state (e.g., the state's Department of Vital Statistics or Registrar of Marriages).

Look for a section related to marriage certificate updates, corrections, or modifications.

You might find an option within the "Services" or "Marriage Registration" menu. 

If you want to do it physically then your wife cn execute a power of attorney authorising any close relative in India to carry out this task by visiting the concerned registrar office and comply with the legal requirements to complete the desired tasks

Correcting the Name on the Marriage Certificate

The Correction Procedure: Indian marriage certificates can be updated or in the said case may be corrected by making an application to the local marriage registrar office in which the marriage was being registered. This is normally done by through the process of submitting an application together with an evidence of the correct name (like the father's Aadhaar card, PAN card, or passport) and an affidavit stating the reason for the error of the same.

The Physical Presence Requirement: Majority of the state marriage registrar offices demand that the applicant or at least one of the parties must be physically present for verification, thumb impression, and witness authentication. This is a standard procedure and a protocol in order to avoid fraud.

Limitations in Online Application: Although marriage registration applications can be started online in most states, corrections generally need offline submission and personal verification at the registrar's office.

If You Are Unable to Be Present Physically in India

You may sign a Power of Attorney in the US naming a reliable relative, friend, or a legal practitioner in India to represent you to file the correction application and formalities at the registrar's office.

A notarized affidavit from wife or the authorized person might be required wherein they are required to explain the error and request the correction. Along with that supporting identity documents of the party will also be necessary.

Contact the marriage registrar office or local municipal corporation where the marriage was registered to confirm the exact documents and process for correction via PoA, by fulfilling the conditions.

Impact on Immigration Petition

Minor misspelling in the marriage certificate, particularly in a relative's name (such as the father's middle name), usually will not make much difference in immigration petitions, as long as the marriage certificate is genuine and valid. You may present an affidavit or a notarized letter stating the misspelling along with the original certificate. Immigration officials generally accept such clarifications as long as the misspelling is slight and does not impact the identities of the parties. Nevertheless, it is suggested that the correction be undertaken prior to the filing of the immigration petition so that no delay or request for supplemental evidence is encountered from immigration officials. A notarized affidavit documenting the mistake and confirming the proper name can serve to temporarily clear up the situation for immigration purposes. A notary document, however, does not substitute for the official change on the marriage certificate. It is a corroborating document, not a replacement.

- You can give POA to any relative in India for approaching the Marriage registrar for the correction of her fathers name 

- Further, if you have given the correct information at the time of applying for marriage registration then the said marriage registrar is bound to correct the same. 

 - However, fathers name cannot be a ground for cancellation of her immigration, hence you need to enquire for the same there.