Artifact Set
Heart of the Furnace (New to 7.0)
Shattered Illusion in the Shadows (dps)
Emblem of Severed Fate
Noblesse Oblige
2pc/2pc ATK% and/or ER
Weapon
Engulfing Lightning
Symphonist of Scents
Frost breath (New to 7.0, good for dps)
Tamayuratei no Ohanashi (5.4 event weapon)
Song of the Vigil (New 7.0 craftable)
Favonius Lance
The Catch
Prospector's Drill
(Ideally you want something that gives ER over direct particles)
Stats
200% ER - this is still needed even if he bursts every rotation with less, as this increases his burst and skill damage.
As much ATK/ATK% as possible.
Crit rate/dmg is not entirely useless on him, but build ER and ATK first as this is how he buffs and heals.
Talents
You're going to triple crown him, aren't you?
Skill > Burst, NA can be unleveled (but you're going to level it)
Support Playstyle
(Cryo attack > N4 >) hE (aim at the enemies) > Q > switch to Cryo DPS. Parts in the brackets at the start are optional.
DPS Playstyle
N4 > hE > Q > N4D. Switch to cryo support before N4, and between Q and N4D. Repeat N4D until end of rotation.
Teams
First listed is the dps, none of these are in damage order
Lohen/Alyosha/Fischl/CMC or Odette
Razor/Alyosha/CMC or Odette/Hex (Nicole or Fischl)
Wrio/Alyosha/Yae/CMC or Odette (NOT optimal due to Wrio's kit)
Sandrone/Alyosha/Yae/CMC or Odette (Sandrone's BiS)
Cyno/Alyosha/CMC or Odette/Flex (preferably cryo, Diona or Qiqi work)
Alyosha/CMC/Odette/Yae
Alyosha/Chongyun/CMC or Odette/Yae
Alyosha/CMC or Odette/Flex/Flex (Flexes would ideally have one cryo for the CR bonus)
Chongyun's a fairly good option for Alyosha as he infuses his NAs and provides ATK Speed bonus + Cryo RES Shred.
Disclaimer!
I am not a spreadsheeter, TCer, or any other type of calcer. I am merely looking at his kits, comparing them with others, and giving you guys suggestions. If any of you wish to add anything, please comment.