In general, here's what is considered to be correct for writing dialogue:
"She was one of my cousins," he said.
All related information for that sentence should go in the same paragraph. That person who's speaking owns that paragraph. Everything in that paragraph is what they're doing, what they're thinking, what they're saying. No one else.
Here are a few things I've seen:
"She was one of my cousins." He said.Why wasn't this good? There should be a comma after 'cousins' and 'he' shouldn't be capitalized. It wasn't a typo in the book I tried to read, either. The entire book was formatted that way, so I finished reading the first page and was done.
Here's another one:
She had to explain.All of that information is in separate paragraphs. They should be in the same one, so the reader knows who's talking in the dialogue. This was so annoying to me, I had to skim the rest of the book so I wouldn't get angry. I'd have stopped reading if the author hadn't been a friend of mine.
"She was one of my cousins."
She knew it didn't make sense, but he had to know.
And, one more:
"She was one of my cousins," said Jeremy.
If you're writing genre fiction in the US (not children's fiction), then it should be 'Jeremy said.'
Thus, if you're writing, study the mechanics, or readers (like me) will throw the book away before getting past page one.
Have a great day!