Working in CTS ,h1b stamped with other employer!Can I ask job in CTS with Visa Stamped

USA H1B Visa
1

Hi.!

I am currently working in -CTS- applied H1B with other employer in USA got stamping Done.

Now employer asking me to search job .

-Can I ask CTS for -Job with my current stamping?-

Is there any way can I work with CTS only with my H1B Visa stamped???

Please Help!!!

2

CTS can apply for cap-exempt petition for you. Once approved, you can travel and work for CTS using CTS’ petition and old visa stamp.

3

Thank u Saurabh.,
how long it will take for filing cam exempt petition.
I heard from one of my manager that CTS is decreasing no of petitions and also not sure about project.

1.In this condition will CTS accept my request?
2.my technology is Java,how is the market for java in USA after EO.??
3.is that safe can I travel to USA and search job now in present situation ??