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If I have the following idea,

The influence of A, B and C to the reconstruction process is discussed in next section.

I am not sure whether I used the correct preposition. I feel I should use "for" (instead of "to") after A,B and C.

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The word you're looking for is on.

The influence of A, B and C on the reconstruction process is discussed in next section.

Influence to and influence for don't make any sense. Influence over is possible, but usually in other contexts. For example:

As an alumni who donates a lot of money to the school, I have some influence over the school board.

Influence over usually means something similar to sway/convincing power; that is, "I can get them to listen to me, and they're more likely to accept my ideas than if it were someone else presenting them."

Influence on is usually used in cases where the influence is more direct, and that's what applies in your case. Another example:

The influence of government spending on the national debt is obvious.

When using influence on, you're usually describing something which definitely causes some factor (such as spending -> deficit, or your reconstruction example).

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