How to verify text on a newly open window which opens after clicking on a link on current window?

Cypress does not support working in a new window. So, you need to open new window in same tab only. For that you can remove the attribute target from the link element. 

Consider this:

<a href="" target="_blank">Welcome to Facebook</a>

Above link will open facebook in new window because of target="_blank" attribute. To remove target attribute you can use below code:

cy.get('a[href*="facebook"]').invoke('removeAttr', 'target').click()

After removing the attribute and using the click function, it will open facebook in current window. After that you can verify the text Facebook helps you connect and share with the people using should

cy.url().should('include', 'Facebook helps you connect and share with the people')