No, you cannot seek the quashing of an FIR solely on the basis of the expiry of the limitation for filing a chargesheet. The limitation period for submitting a chargesheet is applicable only when the accused is in judicial custody.
The limitation period for the submission of a chargesheet is provided for granting statutory bail to the accused under Section 167(2) of the CrPC. There is no provision in the CrPC that allows for the quashing of criminal proceedings due to the non-filing of a chargesheet within the stipulated period.
If the FIR contains a bald allegation or if no offense is discernible from the version of the FIR, you should consider approaching the High Court under Section 482 of the CrPC to seek the quashing of the entire proceeding. It appears that, given the nature of the offense, the allegations can potentially be substantiated through electronic evidence. If the prosecution is unable to retrieve any information related to the email, it is certain that they cannot establish your guilt.
Therefore, in this situation, it is advisable to seek the quashing of the FIR on the grounds of baseless and unsubstantiated allegations or the absence of any offense apparent from the context of the FIR.