This page explains in detail the interactions between the Yoshi series and the Zelda series.
The Legend of Zelda: Link's Awakening
June 6, 1993
(Screenshot from Link's Awakening DX).
Yoshi
Zelda
One of the prizes in the "Trendy Game" at Mabe Village is a Yoshi Doll, which is actually the first item in the Trading Sequence, that must be given to the new couple's son, in exchange for a ribbon. When won, the owner tells that Yoshi "seems to be showing up in many games recently", referencing Yoshi's growing popularity at the time, starring in his first few games. Since this reference doesn't seem to be related to Mario, it's considered a reference to the Yoshi series.
Yoshi's Story
Screenshot from Stage 2-3. "Zelda" can be read many times in the right half of the screen, sideways.
December 21, 1997
Yoshi
Zelda
Stages 2-3 and 2-4 take place in the sewers and are designed as if they were made out of old newspapers. On them can be found, written sideways the name "Zelda", actually in the same style as the series' logo. Other writings include "Yoshi", "Nintendo", "N64", "Mario", "Luigi" and "Pikachu".
Yoshi's Island DS
November 13, 2006
Yoshi
Zelda
The Toadies stealing the babies. Baby Link is in the lower right.
The game's introdution shows Kamek and his Toadies stealing all the babies in the Mushroom Kingdom, and among these is a blonde baby that seems to have long ears. This is believed by many players to be a child incarnation of Link, the hero from the Zelda series.
While this can't be confirmed to be a reference, since the baby has a different haircut than any other appearance of Link, it seems likely since the game also features a Baby Donkey Kong, Baby Wario and an arguable cameo of Baby Olimar from Pikmin.
Assuming this as a reference to Zelda, it counts as an In-universe link since unless it's named oherwise, the baby can be considered an actual, official incarnation of Link.
License
Copyrights for both series are held by Nintendo.