If I jump inside an accelerating train, will I land at the same spot?

You are not wrong -- if the train is traveling at constant speed, then a vertical jump results in you landing in the same spot.

When the train is accelerating, you land in a different spot. Let's say you are facing forward and the train is accelerating at "a" m/s² in the forward direction. At the time you jump, the train's velocity is "v" and your "hang time" is "t." When you land, your horizontal velocity is still v, but the train's velocity is

v' = v + a*t

You have traveled forward

d = v*t

while in the air, but the train has traveled forward

d' = v*t + ½at² = d + ½at²

Suppose the train is accelerating at 2 m/s² and your hang time is ½ a second. Then you land

½ * 2m/s² * (0.5s)² = 0.25 m = 25 cm

behind the spot where you took off.

Hope this helps!

If the train is accelerating then you would land at a different spot.