Which hiv test can give accurate result in short period and it's conclusive and does not require further testing later ?

It is not possible to have 100% conclusive testing until about 6 weeks after exposure. At that time, a negative antigen-antibody test (AgAb, combo, 4th generation test) is conclusive. Earlier testing can be highly reassuring, however, especially with an average (not very high risk) exposure; and PCR to detect viral RNA can be done at 2 weeks if necessary. But these never are truly conclusive.