What is the Yukawa potential converging to zero? Afaik the strong potential rises with the distance between quarks, hence, it should rise accordingly.
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This is an answer to the question v3.
The Yukawa interaction was usually thought to describe nucleon-nucleon interactions (nucleon = proton or neutron). Nowadays, one cannot view it as a fundamental model for quarks and gluons.
In order to derive the Yukawa potential, you need to consider massive spin-1 bosons (Yukawa initially thought of pions mediating the strong force between nucleons), as indicated in this question.
Finally, yes, the strong potential between quarks and gluons is (assumed to be) linearly increasing, but this has nothing to do with the Yukawa potential between nucleons.
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