I am really no expert in Hebrew grammar and I know there are many variants of same word. In particular I think there is no tradition for the puntuaction of the Mishnah.
However in my siddur (Panzieri, Italian rite) I noticed that שירי הדם, in the Mishnah of "Eizehu meqoman shel zevachim" is spelled שִׁיְּירֵי, while in all the other siddurim I have seen so far it is שְׁיָרֵי. What puzzles me in the version of the Panzieri is the "sheva + yud" form that I have not thought to be possible. Can I assume that the form Panzieri is incorrect or is it an admissible variant?
In order to prevent rendering issues I write here the two forms in full:
Panzieri = shin with hirik - yud with dagesh and sheva - yud without puntuaction - resh with tzere - yud without puntuaction
Regular = shin with sheva - yud with qamatz - resh with tzere - yud without puntuaction