What should be the labels for subword tokens in BERT for NER task? For any NER task, we need a sequence of words and their corresponding labels.
To extract features for these words from BERT, they need to be tokenized into subwords.

For example, the word 'infrequent' (with label B-count) will be tokenized into ['in', '##fr', '##e', '##quent']. How will its label be represented?

According to the BERT paper, "We use the representation of the first sub-token as the input to the token-level classifier over the NER label set".

So I assume, for the subwords ['in', '##fr', '##e', '##quent'] , the label for the first subword will either be this ['B-count', 'B-count', 'B-count', 'B-count'] where we propagate the word label to all the subwords. Or should it be ['B-count', 'X', 'X', 'X'] where we leave the original label on the first token of the word, then use the label “X” for subwords of that word.

Any help will be appreciated.
Method 2 is the correct one. 

Leave the actual label of the word only in the first sub-token, and the other sub-tokens will have a dummy label (which in this case is 'X'). The important thing is that when calculating the loss (e.g., CELoss) and metrics (e.g., F1), this 'X' labels on the sub-tokens are not taken into account.

This is also the reason why we don't use method 1 is that otherwise, we would be introducing more labels of the type [B-count] and affecting the support number for such a class (which would make a test set no longer comparable with other models that do not increase the number of labels for such class).