I recently suggested in a post that Verin and Sheriam were both in the Supreme Council of the Black Ajah and some people were sceptical [link below].

During a re-read of TGS I found a clue to prove this:

When Egwene accuses Sheriam of being a BA and Sheriam at first negates it, it's said:
"Prove it, Sheriam. The woman who came to me in the Tower gave me your name as a leader among the Black Ajah ."
Sheriam met Egwene's eyes. "Ah, then," the woman said softly, eyes mournful. "Who was it, now, who came to you?" "Verin Mathwin." "Well, well," Sheriam said, settling back on her chair. "Never expected it of her , I'll say. How did she get past the oaths to the Great Lord?" "She drank poison," Egwene said, heart twisting. "Very clever." The flame-haired woman nodded. "I could never bring myself to do such a thing. Never indeed." [emphasis mine]

Sheriam was a leader of the BA, which must mean that she sat in the Supreme Council. Since she knows that Verin is a BA, too, and states that she never would have suspected a betrayal of her, it makes sense that Verin was even higher-ranking, most likely the third or fourth highest BA (the second highest was Galina).

It seems obvious that Verin's notes contain the members of the Supreme Council, since she said about her notes:
"Names, locations, explanations, [...] Everything I learned about them. About the leaders among the Darkfriends, about the Black Ajah. The prophecies they believe, the goals and motivations of the separate factions. Along with a list, at the back, of every Black Ajah sister I could identify." Egwene started. "Every one?" "I doubt I caught them all," Verin said, smiling. "But I think I got the large majority of them. I promise you, Egwene. I can be quite thorough."

Egwene also says about Alviarin:
"She's Black,[..] And near the head of their organization in the Tower. This was the information Verin died to bring me."

I think Verin could only get this informations about Alviarin and Sheriam being leaders, if she sat in the Supreme Council herself.

That Egwene thinks, though, that Alviarin is only "near the head", not the Head, might indicate that Verin just knew that Alviarin is in the Supreme Council, but curiously didn't positively know that she is the Head (or Egwene's statement was a bit imprecise here).