Tshissamᵘ uiash. She cooks meat.
Tshissamueu utauassima uiashińu. She cooks meat for her children.

The verb tshissamueu is an applicative (benefactive) verb. It’s formed by adding the suffix –(a)u to the stem tshissam- followed by the transitive animate verb final -eu, which adds a participant, here the beneficiary of the action, nitauassimat the children.

Here are some examples in the first person:

Nitshissen uiash. I’m cooking meat.
Nitshissamuauat nitauassimat uiashińu. I’m cooking meat for my children.

Other examples of applicative benefactive verbs (VTA):

VTA (applicative)
petau (VAI+O) she brings something petueu she brings something to someone
mitshiminamᵘ(VTI) he reserves something mitshiminamueu he reserves something for someone
nimishtamᵘ(VTI) she dances in honour of something nimishtamueu she dances in honour of someone
takunamᵘ(VTI) he holds something takunamueu he holds something for someone
mashinaimᵘ(VTI) she writes (something) mashinaimueu she writes (something) to someone

The conjugation of applicative verbs with the suffix –(a)u is distinct, because the -a appears in the inverse forms.

tshimashinaimun you write me tshimashinaimatin I write you

Note the difference between the homonyms petueu bring something to someone and petueu hear someone.

VTA applicative petueu VTA regular petueu
tshipetun you bring me something tshipetun you hear me
tshipetuatin I bring you something tshipetatin I hear you

For more information, consult Grammaire innue (Drapeau, 2014: pp. 224-230).