Need information about SBI Clerk

Providing a piece of wrong information will be treated as a fault and your candidature can be liable to be rejected. That is why we should be careful while filling the application. All now depends on the authorities.
You might have submitted all your certificate copies with your application. In that, your second language might have been mentioned. In your application, you might have mentioned your local language. If they go through these points carefully they will find the mistake.
What is the Present Status of your selection? Certificates verification is over or not? If certificate verification is over and there is no problem means you need not worry.
The eligibility criteria say
"Candidates should have verbal and written proficiency in the official language of the State/UT. The candidate should be able to read, write and speak the language"

There is no rule that you have to study the local language in your 10th or 12th class. So they may not reject your candidature.

Anyhow I suggest you send a letter stating that by mistake you have committed that mistake but not intentional If you have studied your local language in some other exam and if you have any certificate to that extent you can attach that and sent to the concerned authorities as given in their notification,

Suppression of a mistake while filling up an application form relating to an organisation is treated as a sort of indiscipline and for such a lapse the candidate is liable to be rejected . However, you have to ensure whether such a stage of certificate verification is still to come up or it has already been over.
In case, it is already elapsed, you have not to think over that line but pending of this process may precipitate your your fault. You can avert such an ugly situation with enhancing your efficiency to a manageable extent by undergoing a little practice in course of reading or writing the Hindi Language. You may use the gap period for strengthening your language to restore your confidence.You should not show any guilty during the session of verification. In that way, you can avoid this embarrassing situation with your tactful display of your wisdom.

Before this point comes up for scrutiny and clarification is asked from you during the verification session, it will be better to inform them about this. I will advise you to go to IBPS site (Institute of Banking Personnel Selection) and find out their contact details and immediately write an application and try to send it from both the modes as email as well as physical mail to the examining body that such and such mistake had been there inadvertently by you while filling the form and you do not know that language but are proficient in Hindi. Keep a copy of this correspondence with you so that at the time of document verification you can show them that you could spot your mistake in time and were genuinely concerned to intimate them.

The verifying authorities will use their judgement in the case and may be that they may sort list you for those states where Hindi is the medium in the Bank working. So be patient and inform them and prepare for the document verification session. Mistakes can happen in our lives and the authorities always see that if it is not a major one and can be accommodated then they always think in favour of the candidate.

Clerical vacancies in banks, the selection and filling are usually State-wise. Such posts necessitate frontline jobs needing direct contact and communication with people. Hence it may require proficiency or at least working knowledge in that local language. That is why they put the condition of knowledge of local language. Moreover, the applications, chalans, and sometimes even cheques are filled in local language. So, most clerical jobs require knowledge in local language.

Sometimes candidates just send their application preferring a particular state when the vacancies are more than other places. In major metropolitan cities and major urban centres one can manage with knowledge of English and Hindi and picking local language by experience. This is not possible when the posting is in interior villages or small towns.
In your case you say it happened by an inadvertent ticking on the slot for local language.

If you are already selected for posting then just face the situation and go ahead.
Anyway don't panic. If it is a genuine mistake, you can tell about it when you are called for joining. Alternatively if you have sufficient time for joining, try to learn the language at least to the level of speaking and understanding.
You can also contact the relevant office that deals with posting. You can convince them and get their help in this regard. They may accommodate you in the offices or seats where you need not directly deal with public. They may help you to give a posting in a suitable place/office where you will be able to manage. For example they may post you in some back offices or Regional Offices etc where you are not needed contact or communicate with public. Then you can work hard to learn the language as early as possible. If needed you may also seek help of the employees union people who also may be able to help you.

Hence do not worry unnecessarily. However if you have any doubts or misapprehensions in mind, keep applying for other similar suitable jobs in the meantime. You will be getting what is destined to you. But be careful in future while filing up forms and furnishing bio- data. Give only facts and truths.
Best wishes.