... but in shortest interval of time the particle is just forward from its initial position.
What is the "shortest interval of time?" 1 second, 1/10th of a second? 1/100th of a second? 1/100000000 of a second? In Newtonian physics, we consider an interval of time that is infinitesimally small. The handling of this sort of thinking is actually what made Newton and Libnitz's Calculus so terribly powerful. For thousands of years, we grappled with how to calculate with infintessimally small units Zeno's Paradox is a famous thought provoker along these lines. The Calculus of Infintessimals (now just called "Calculus") was the first to resolve these issues consistently in a way which correlated to how you and I view reality.
In the calculus, the slight forward motion of the particle is captured with a variable like "dp", the infinitesimal shift in position. When we do this, we find that the effect of this forward motion on the force does not lead to a dragging effect from the centripetal effects.
Of course, don't take my word for it. That's what the calculus says will happen, if you just sit down and crunch the numbers using those rules. The thing that made Calculus famous was that the formulas that arise from crunching numbers the calculus way do indeed tend to mirror what happens in reality. You can create calculus equations that don't mirror reality, we simply elect not to teach those in physics classes. To the best of our understanding, the behavior of the world around us can indeed be modeled with calculus, if you get the right equations.
Now there is a second half to this. You talk about a "centripetal force," but how do you know it is perfectly centripetal? "Centripetal" is actually a description of the force. There is some force (perhaps the tension of a wire or gravitational attraction), and we observe that that force acts in a centripetal way.
So if you have a physical situation where this "centripetal" force is causing a dragging effect on the object, then it isn't really "centripetal." Much of engineering is dealing with this: when can we just assume that a force behaves some convenient way, and when do we have to model all the real interactions which make things fuzzy. But if we define "centripetal" in Newton's way, and turn the crank on the calculus, we find that this centripetal force indeed does not slow the object down at all.