After how many days of FIR can we file case in the court

If the accused arrested then Police have to produce him before Magistrate within 24 hours. If police have not arrested him means police is still investigating the case. There is no time limit for filing of a charge sheet though if an accused is in police custody or in judicial custody he is entitle to bail if charge sheet is not filed within 60 or 90 days under 167 Cr.P.C.

If you are aggrieved with police then you can always file a private complaint with Magistrate under 200 Cr.P.C. Good luck

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Learn what are cognizable and non-cognizable offences and the difference between them with the help of this criminal law guide of India.

Hi
Any FIR filed under 420 case is a cognizable offence.
Generally, cognisable offence means a police officer has the authority to make an arrest without a warrant and to start an investigation with or without the permission of a court.
So, not sure why police want to take cognizance of the offence with the permission of court.
Courts generally take cognizance of such offences within 24 hours.
You should apply to High court and ask for directions for registration of FIR and commence investigation.

if any first information report is received it must be sent to court within 24 hours from the date of registering the crime. please see whether any receipt is given to you or not or else please encrypt your complaint in a white paper and register post to the concerned police station, superintendent of police, local magistrate having jurisdiction and district collector then only it will get registered and you can get justice