Trademark series is not a legal term, and there is no related concept in trademark law.

This should be a language habit or a saying in China. As far as I understand it, it is a series of identical, similar or related trademarks, a collection of more than or equal to 2 trademarks.

For example: Wahaha series trademarks are a collection of the same trademark series. Most well-known trademarks are registered in many categories, so a trademark series with the same name is produced;

Another example: Peony, Yellow Peony, black peony... are similar trademark series;

There is also a company that has multiple trademarks across industries, so these different trademarks are the company's trademark series....

It can be seen that trademark series is not a term or legal term, it is just a name or expression for a collection of multiple trademarks.