Hi, SSN is required field for my wife. But her visa status is H4 so she doesn't have SSN. How should I fill in SSN number field for her?

[LinaJ2018]

You should leave it blank.  

You might need to apply for an ITIN for her.  Per IRS, if your spouse is a nonresident alien, he or she must have either an SSN or ITIN  if  :

1.  You file a joint return or

2.  You file a separate return and claim an exemption for your spouse, or

3.  Your spouse is filing a separate return.

For filing status, you can file either Married Filing Jointly ( see  Nonresident to resident  ) or simply Married Filing Separate.

[ In the TurboTax program, you would follow the step-by-step interview questions to choose the appropriate filing status, enter your spouse information and leave the SSN blank, after print out the return , you can leave it blank or hand-write APPLIED in the space.]

If you want to file Married Filing Separate, you can qualify for an exemption for your spouse only if:

 - Your spouse had no gross income.

-- Your spouse won't file a tax return.

 - Your spouse didn't qualify as the dependent of another taxpayer.

Additionally, you cannot e-file a tax return which does not include a SSN or ITIN.  If you fall under one of the above conditions, you will have to manually apply for an Individual Taxpayer Identification Number ITIN on Form W-7 for her.  

See https://www.irs.gov/Individuals/General-ITIN-Information.   

Although you cannot e-file, you can still use the TurboTax program to prepare your tax return and required forms. Then print, attach to the Form W-7 with the required documentation ( see the above link ) and submit everything to the IRS Austin location in Texas by mail.