Statement - I : Two balls of different masses are thrown vertically upward with same speed, they will pass through their point of projection in the downward direction with the same speed. (neglect air resistance)
Statement - II : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

Let the balls be thrown vertically upward with speed  u.

Using ${\left(0\right)}^2-{\mathrm{u}}^2=2(-\mathrm{g})\mathrm{H}$, we get the maximum height attained by the body.

After reaching maximum height the body will freely fall,

${\mathrm{v}}^2=2\mathrm{g}\left(\frac{{\mathrm{u}}^2}{2\mathrm{g}}\right)$

$\Rightarrow \mathrm{v}=\mathrm{u}$

As a result, the balls will fall through the projection point at the same speed (v).
The highest height and the downward velocity achieved are independent of the ball's mass, according to the formulae that were used.