"My questions are....
1-Does job title need to be exactly same as suggested is Codes of Practice?
2-Is it possible for HR dept to allocate COS code from Level-6?
3-Just want to reconfirm that I can't move from Level-6 to Level-4?"
Check out this guidance:
https://www.gov.uk/government/uploads/s ... 5-2017.pdf (from page 118).
Also, you said that the company said that you scored the highest, but basically, the company MUST give preference to a settled worker/permanent resident/British citizen if this person meets the minimum requirements; it doesn't matter that you have better qualifications.
"...you
must appoint the settled worker
even if the migrant is more skilled or experienced. The
only exception is if the job falls within one of the
PhD level standard occupation classification (SOC) codes listed in Table 1 of Appendix J of the Immigration Rules; when you can appoint a migrant if they are the most suitable candidate."
For eg.:
Job asks for a BSc and 3 years experience
i. British citizen has a BSc and 3 years experience
ii. you have a Master's and 8 years experience
Even so, the British person is
supposed to be employed because they meet the
minimum requirements.
Do not quit your current job. Try to read and understand the guidance and ensure that all your ducks are in a row.
Best wishes.