One External HDD locked&encrypted by BitLocker,later the Ext. HDD not accepted the BitLocker key, no recovery key available how to access the Ext.HDD?

All data on the external HDD is encrypted. Data recovery will only get you encrypted data. Only way is to get the recovery key from the formatted laptop. You may try to recover the recovery key from the formatted laptop using any data recovery software like Recuva. If it doesnt help try professional data recovery software on the laptop. Only solution is to get the recovery key back.

Currently no one can break the encryption on bitlocker.

Try to recover the recovery key from the laptop. By install recovery software on external HDD then scan the internal drive for the recovery key file

Take the drive to a data recovery specialist who should be able to use a hardware solution such as (Salvation Data) to remove the password or in the least be able to perform an extensive/intensive forward/reverse scan of your drive to recover the data.

Please try like this,

Install BitLocker in another machine.

Then Copy the recovery key file from that machine. and keep in your computer

Change the name of the file  to your computer name.