Dear Amol,
Did you check the validity area between "Customer Specific Label" and "Generic Label", either at labels assigned in material master level or at the generation variants level if not maintained at material master level?
a. If the validity area is same, then there should be something else which prevents "Customer Specific Label" being listed. Please check if you can find any information in Label determination log.
b. If the validity area is different, check the number of countries assigned to each validity area. I suspect that the validity area assigned to "Generic Label" has less countries than the validity area assigned to Customer Specific Label". Hence, validity area assigned to "Generic Label" took precedence over the validity area assigned to Customer Specific Label" and prevented "Customer Specific Label" being listed. You can validate it by assigning the same validity area to both labels. If it works fine, then it is issue with the validity area used for both the labels.
Thanks and Regards,
Kannan Veerapandian.