My roadbike has a mix of components. It has shimano claris r2000 fd and crankset and everything from sti's, rd and where all for 10 speed. The problem was when Im on any 3 small cogs on the back and I shifted my fd to the small chainring, the chain would not engage fully and I always ended up spinning the cranks but not transferring any power to the cogs. I hope that you guys can aid me in my woe.

(Never mind - thought you had a triple crankset.)
Does the chain drop between the two chainrings or off the inside of the inner ring?

You might want to try this on the Bicycles Mechanics sub forum.

https://www.bikeforums.net/bicycle-mechanics/

I had symptom like that when trying to use 11 speed chain on 10 speed set up-

chain would spin between the chainrings.

In my case, I used 10 speed chain on 8 speed crank and it keeps dislodging everytime I down shift while cross-chained

Where does the chain dislodge to?
How many cogs in the rear? 10? "My roadbike has a mix of components. It has shimano claris r2000 fd and crankset and everything from sti's, rd and where all for 10 speed."
A 10-speed crank/chainrings can be adjusted for use with a wider chain by using shims but to adjust for what you may be dealing with would require careful use of a file on the crank to move the rings closer together. (??) Or a different (10-speed) crank.

It is a combination of several factors. You have a crank with 8 speed spacing between the rings along with a derailleur designed for an 8 speed shifter which will move the chain a sufficient amount to engage properly at that spacing. However, you are using a much narrower chain along with a shifter designed to move the chain a sufficient amount for narrower chainring spacing. Consequently the chain doesn't move far enough to engage the inner chainring especially when you are on the smallest cogs in back

I was planning to buy a tiagra fd. I hope it'll solve my problem

Which 10 speed STI shifters do you have? Current Tiagra 4700 front derailleurs will not work correctly with any other 10 speed shifter

I've got the 4700 ones paired with claris r2000 front derailleur

Sounds like the front derailleur is not moving in quite far enough to push the chain to the small chainring. Unscrewing the "L" screw 1/2 a turn may solve it. Also, the angle of the front derailleur relative to the chainring might be slightly off.

However, unscrewing the "L" screw a bit, may cause it to overshoot the small ring when on the larger rear cogs, due to the chain line.

I have a similar problem on one of my bikes that uses a 10 speed chain with a "5 speed" crankset & front derailleur. Since I have mis-matched parts, I accept that shifting is not perfect, and I have to make allowances, such as shifting the front more carefully, depending on which gear I am in.

For instance, when on the smaller rear cogs, and shifting to the small ring, shifting quickly can give the chain more of a push to get to the small ring.
When on the larger rear cogs, and shifting to the small ring, I shift the front more slowly, to avoid overshifting the small ring.

I often bring a few tools on rides when first setting up gears, so I can stop and make minor adjustments.

I would so pay you money to say that three times fast.

Good explanation, but boy is that a mouthful.