There are a number of ways you can give medication, and partly the choice can depend on the hamster, their personality and how unwell they are. Some find it far to stressful to be held and have it administered directly. And if done incorrectly there can be a risk of it going down the wrong way and causing choking. Some will spit it out again.
The other two methods are - sucking a bit of ribena or runny honey into the syringe with the meds, as Beryl suggests, and some hamsters will then happily lick it from the syringe without you have to handle them. Others will run away or bat the syringe away.
So the next method is the putting it in food method, as Elusive has mentioned. For Metacam this isn't an issue as it tastes nice. For Baytril, it tastes nasty and hamsters will still reject the bit of food if they can smell or taste the baytril, so it needs to be something strongly meaty flavoured (usually) to disguise the taste. Babyfood often isn't strongly tasting enough.
One that has always worked for me, was recommended by an experienced breeder - and it works so well the hamsters demand more lol! And get quite annoyed when you stop giving it.
It's a particular beefy dog food for small dogs called Country Hunter beef. It's in small pouches that you can keep in the fridge so you can get 3 days worth of dose out of a pouch. The rest will need to be discarded then, unless you have a dog to give it to.
It looks a bit like corned beef in jelly but is mostly meat and quite firm and not runny. About a pea sized amount on a little dish (eg a jar lid). Put half a pea sized amount, then drop the meds on top, then the other half sized pea amount on top. You need to be careful that the meds stay on/within the food and don't run down past it onto the dish - to make sure they get the dose. So you can ensure there's a tiny dip in the middle before dropping it in.
I'll link it below but you may need to get hold of something quicker if it's not available locally.
It's really important they get the full dose and giving it twice a day isn't easy due to a hamster's sleep patterns (unless you're an early riser!). If Reggie and you are up at 7am you could give the first dose then and the second at 7pm. It's not really possible to fit in two doses a day unless one is given early morning when Reggie is awake as he'll be asleep during the day. The early evening dose in food, they sometimes eat a bit and then come back and finish it off later, but that's ok.
Natures Menu Country Hunter dog food - beef.
Corned beef may actually work as well, but I haven't tried it. I did see someone on youtube once who tried all sorts (but not meaty food!) and found a bit of prawn cracker with the meds on was accepted. However they can be quite salty and maybe not the healthiest option.
Whilst this is also giving quite a lot of protein it is only for a very short time and in very small quantities. Some people will say dog foods shouldn't be given to hamsters, but this one has minimal basic ingredients and actually smells very tasty! And again it is just a short term thing.
I use a wood skewer or cocktail stick to sort of mix the meds in with it as the amount is so small.
You could try runny honey or ribena in the syringe first (just a tiny amount) and see if he will lick it from the syringe.
Bite looks painful!