Without looking deeply, I suspect that the problem is that for each of the multiauthor papers sharing a first author, the subsequent authors are different, so Endnote doesn’t combine them and so you hid the second citation authors to rectify this. The options box for that should say "Consecutive citations by the same Author s" as that still treats them as two citations and therefore the inclusion of the semi-colon if any of the subsequent authors vary. (Very frustrating - this lack of conforming to the expectections of authors and journals.) If a semi-colon isn’t required by the style, separating citations, you can change them all to a comma, but it will change them all, and that too is unlikely to conform to the requirements of the journal.
The only way I know of, to get exactly what you want, is to completely hide the second author and year, and type in the comma year into the edited citation suffix.
I appreciate your reply very much. I tried it according to your smart solution, and found that there is still a problem: an extra closing bracket, as shown below
It can be complicated when you are using the Author (Year) which should look like this Author|*(Year) (where the * is actually a tiny diamond and is the “link adjacent text” character from the insert field dropdown) – but even then I still see the left over parentheses, albeit, both of them. Instead of exclude author and year, try show only in bibliography for the second citation.
Author (Year) was likely never trouble shooted for multiple citations as it would rarely be used in that way.