Can the mitzvah of Shiluach hakan be performed with a Blue Jay?
The general rule is that if the bird is essentially kosher, even if we d not eat it because it doesn’t have a mesorah, then shiluach haken should be done. However if the bird does not have kosher simanim, then it should not be done. It seems that lue Jays are not a koher type of bird, therefore you should not do shiluach haken on it.
Hisorirus Teshuva 4-155, Birkei Yosef 292-10, Shalayach Tishalach – Dinei Shiluach Haken 14.