When I try to check the serial number of a product, it shows an error

There must be something about that serial number or device which Apple's website has an issue since I get the same error. I tried my own iPhone serial number and had no issues. You will definitely need to contact Apple to see what is going on there as @Ronasara suggested. I initially mistyped the serial number and the website recognized the serial number was wrong.

FYI, you should not post your serial number online since it is considered personal information. Some unscrupulous person may use it against you or try to get more personal information about you. I'll ask the moderators to edit your post to remove the serial number.

You might try asking the question to that product's vendor.