Withdrawal of criminal and civil complaints against family.

The civil case can be withdrawn by the person by filing a memo to withdraw the same.

If the police has already registered FIR and if it is a compoundable offence then the defacto complainant can file a petition before trial court to compound the case owing to compromise and out of court settlement.

If it is non compoundable offence then you may have to file a quash petition before high court and the defacto complainant has appear in person before high court and file an affidavit expressing no objection on the basis of compromise settlement.

You may consult your lawyer and proceed as suggested.

You have stated, inter alia, that,

"Due to a family dispute, the  family members have filed some criminal and civil complaints in police station.

There are no FIRs though. 

Their is no case filed in court."

What is the family dispute ?

What are the civil and criminal complaints filed in police station ? Which police has entertained a civil complaint ?

Further when there is no FIR and no case filed in court, what is the problem ?

When there is no case in any court or police station what is there in Mediation Centre of High Court ?

Pure hypothetical and time pass post.

Family dispute comprises of a son and daughter-in-law being thrown of house by using illegal force. Both parties filed several complaints in police station, but police did not acted on it, stating that it is family matter.

First party then filed a pre litigation mediation in high court, asking for their share in family business and properties.

This is already settled through high court mediation cell (samadhaan) and a settlement deed is issued by them.  

But Police is saying that withdrawal procedure is not available with us.

The problem is that one party feels that the other party may still pursue the complaint after settlement. Also once party want to go to USA and pursue higher studies, but is afraid that due to these criminal complaints lying in police station, despite settlement, their may be a future rejection of Visa or failing of background check. What is the best remedy to ensure that the both these problems are solved to ensure peace of mind ?

Without any complaint before police there's no reason to request the police to permit you to withdraw the non existing complaint. 

Besides in the absence of any criminal case pending before the court or in the absence of any restrictions by an order of court to travel abroad,  there's no reason to be so much anxious about this topic. 

Problems sorted out through court mediation without registering any case against each other should not be any reason for your curiosity over it to this extent.