Archmage of Echoes

• WOTC Official Reminder Textofficial rules
  Ward — Whenever this permanent becomes the target of a spell or ability an opponent controls, counter it unless that player pays [cost].

• WWizards of the Coast2023-09-01
  Official Ruling
  The copy remembers any decisions that were made for the original spell as it was cast, including values chosen for X in its mana cost and whether any alternative or additional costs were chosen. For example, if the original creature spell had kicker and its kicker cost was paid, the copy will also be kicked.
• WWizards of the Coast2023-09-01
  Official Ruling
  A resolving copy of a permanent spell becomes a token, so the token isn't "created." Effects that care about a token being created won't interact with a token that enters the battlefield from Archmage of Echoes's ability.

Rulings via Scryfall