I am writing with a question how I can check the authenticity of the purchased processor.
Is there anyone who can confirm by the serial numbers of the processor
The serial numbers should be searchable and point to the model of CPU indicated on the lid. There was a case recently where someone bought a CPU and someone had actually swapped the lid from a Ryzen 3700x onto an AMD3+ type CPU. The pins were the giveaway.
This link from AMD will show you if you have an authentic AMD Retail Box with a authentic processor inside: https://www.amd.com/en/support/kb/warranty-information/pib-authenticity
Plus you can always open a AMD Service Request under "Warranty" and find out if your Serial Number is authentic from here: https://www.amd.com/en/support/contact-email-form