I was on married status in 2019 but separated since 3rd June 2019 not living with my spouse, Under what status I should be filing my 2019 tax? Should I files as Single?

If you were still legally married at the end of 2019---and it seems that you were -- then your filing choices are to file married filing jointly with your spouse's agreement, or to file married filing separately.  You cannot file as "single" since you are not single.

Your spouse is faced with the same choice--so come to an agreement.

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately