How can I travel US after 3 years If my USA asylum request rejected?
No. Asylum fraud is an absolute bar to admission. Furthermore, those records are readily accessible by practically every country on the planet. Nobody trusts you, nobody wants you. BTW, asylum is a once in a lifetime prospect, and you are permanently barred from ever making another asylum claim anywhere in the world. You're restricted to your country of citizenship - permanently.
You would be required to apply for a visa, which is likely to be rejected
You do it by getting a visa.
You will not be able to. No country will trust you now.
you can apply for a business visa if your asylum is rejected
Your only option is to come illegally.