I have an idea! (first one)

On Hit: 75% of damage done returns as health
No clip required, uses energy
+30% projectile speed
Energy can be used for 6.5 seconds of continuous fire

-25 health
-10% accuracy
Energy fully recharges after 10 seconds
+15% vulnerbility to all damage types

+100 crit chance on enemies with damage increasing buffs
+inifinite ammo
+20% slower fire rate
-speed decreased by 15% when firing

May I make a suggestion?

-Tracer projectiles
-100% Slower reload (I think a pump animation) Medic reloads really fast so
-No random critz
-2% Ubercharge dergrade while in use ( 2%/1sec) Will not funtion without any charge avalible
-15% Slower ubercharge rate ( to counter some effects of the vacc, Kritz, and Quick)

+20% Faster projectile speed
+15% Damage bonus
+Hit animation
+Slowly heal allies within a short radius while in use (Dosen't stack with other boosts, same Particle effect as the Amputator)

..................................... I might be overthinking this a bit................ I just like Medic :D

Perhaps...

Fires lasers that stuns the opponent after every 10 shots fired is rapid succession (Kinda like the bonk that the scout does)
+50% Faster Firing Speed
+Does not require ammunition, but has that type of "ammo" like the Pomson or Manmelter.
+10% Health Recharge Rate
+30% Accuracy
- 30% UberCharge Rate
- 15 Health
- 10% Damage to all persons and buildings

i got a perfect idea dose 40 dmg slows enemys down and has unlimted ammo 5% fireing speed so the total fireing speed would be 50 3 hit kill to kill eny building crits 500 dmg

Does not use ammo
Projectiles can not be reflected
+30% slower reload time (over heat)
No random crits

+25% damage bonus
+every 4 damage healed by your medigun or amputator loads a shot for this weapon (up to 75)
-weapon starts with no ammo
-can only get ammo by healing
-fires tracer rounds

Sorry to pop-in announced:
+ Projectile penetrates players.
+ No ammo necessary.
+ Damage increases 2.5% per Übercharge rate, up to 25%.

- Can only fire 5 consecutive shots, and has to cool down.
- Reduced speed while firing.

Energy shots
+Doesn't require ammo
+Ammo reloads when not in use
+Shoots a laser beam, shooting straight and reaching log ranges
+Damage doubles every moment it is held onto an opponent
-99% Damage
-Speed slows gradually when being used
-When target leaves the beam, damage is reset
-if ammo is fully depleted when in use, weapon explodes violently, damaging the medic and anyone nearby

+15% damage bonus (compared to crossbow)
+infinite ammo
-reloads only while unequipped
-150% reload speed (compared to crossbow)
-lasers leave a trace (like machina)
-One shot per "clip"

Note: I dont want this to be a spammy weapon if it deals more damage.
Death animation can be something like the Pomson 6000 or Phlogistinator

EDIT: I didnt notice it was based on the syringe gun, but what if we make it like a crossbow?

I think it should be:

- Hurts you when used underwater
+ Doesn't require ammo
+ Blurs screen of victim for 2 secs
- Tracer rounds
+ Minicrits wet enemies

how about valve makes the stats
sounds good
goe do better stuff like play the game

You guys are all overthinking it. Not even the Vaccinator is as complex as some of these suggestions.
Just make it a Pomson/Righteous Bison for Medic.
Basically the Crusader's Crossbow without the damage over range or healing effects and
+Infinite ammo
+Penetration
+On hit on Teammate: Extinguishes fire and/or removes Jarate and Mad Milk effects
-Reduced damage (Base damage of about 50-40 sounds good)
-Lasers leave a trace (like Machina)
The death animation should be that of the Engi/Solly Grordbort Weapons.

+200% projectile speed
+doesn't use ammo
+penetrate mutiple targets
+alt-fire: at cost of 50% ubercharge fires a continuum laser for 5 sec that deals +100% damage
+crits on wet players
-20% damage
-tracing shots
-no random crits
-10% speed while shooting (-30% on alt-fire)

Going off of the Ogrelord's suggestion,

+Infinite Ammunition
+Projectiles Penetrate Enemies
+On hit Teammate; Removes Fire, Jarate, Mad Milk, and Bleeding effects
-50% Less Damage
-Projectiles leave a trace