When you deposited amount in protest in court you must have received acknowledgment from registry of deposit of funds 

appeal would be heard on merits and then disposed of 

In event you succeed and appeal is dismissed you would get refund of your money from development authority 

1. it is not clear what the decree of the trial court.

2. if it was suit for specific performance and delivery if possession of property then file execution case in the lower court so that the decree would be implemented in letter and spirit.

3. Since there is no order of stay in operation by the high court, you can  proceed with the execution case.

4. i wonder why your advocate there did not advise this till now. 

You have paid said amount in protest 

you can file consent terms in HC in pending appeal that since amount has been paid to development authority appeal be dismissed 

You can mention same before the high court and the receipt can be produced before the court and can seek a final hearing date to decide the matter on merits. 

Receipt of deposit can be produced before court, court can take that on record.

The court will look upon the merits of the case it wont dispose same based on your application generally. 

You should file a copy of the document in court where the payment under protest made to the the development authority can be proved, but the the court would not consider any such application and would try the case as per the set procedure only.

It's completely clear from your query that the payment has been made to the development authority and not the court 

The chances of your application being allowed are less.

Why have you deposited when have won the case , now court can impose cost on you that even after getting relief from court you accepted the recovery imposed on you and wasted court time by filling case.

yes you have done the right course. it will be dismissed on merits

Since the appeal has been restored by the high court, you may closely watch the hearing date or the listing date and file a memo about this deposit also before you file your counter to the appeal and in the counter to the appeal you may state the grounds and the strong reasons and your objection to the appeal and get the case dismissed ion merits.

you may file a memo along with the photo copy of the payment deposit made with the development authority before the high court in the said appeal to register the same or you can add the same in your counter to the appeal accordingly.

Yes, you can present your argument on that line especially when the development authority side pleads that the respondent had not made any payment, the documentary evidence of the photo copy of the deposit may also be produced before the appellate court.

Move a additional affidavit before the Hon'ble High Court praying that you have paid all the pending dues amounting to Rs.311000/- which was claimed by the DA and now there remains no issue so the case be decided accordingly, automatically the court will issue summons to them for status.

Yes the amount deposited by you can be brought before court through separate application.  However the case shall be decided on merit but you can file application for speedy disposal. 

Dear client 

I don't understand if you have filed the recovery suit for 311000/- rs and you have won the case both in lower court and session court then why have you deposited the amount with development authority. Who gave you the advise for depositing the money if you have already won the case. 

Yes you can file an application for dismissal iof the appeal 

Share the copy of entire documents for a more concrete advise 

If you have already paid the disputed some and did not wish to take it back ones the matter is decided on merits, I think no cause survives in your matter; and thus you should get your case dismissed as non infructuous. 

If you have no intention of getting back your money, your case is infructuous. 

1. As per the information mentioned in the present query, makes it clear that despite of winning the case you have already deposited the disputed amount with the authority.
2. Yes, you should move an application before the court of law stating that you have already given the money and now want this case to be ended, but not surely stretched further.
3. Though you can give submissions orally also, but would be good if move an application for the said purpose along with the copy of any receipt, if received by the authority.