There is no special "new homeowner credit" the first time home buyer's credit expired in 2010.
You can deduct mortgage interest and property taxes on your home. Those are itemized deductions and you get no tax benefit from itemized deductions until all of them added together are more than your standard deduction.
2016 Standard Deduction
Taxpayer under 65, not claimed as a dependent
$6,300 for Single
$12,600 for Married Filing Jointly, or Qualifying Widow(er) with dependent child
$9,300 for Head of Household
$6,300 for Married Filing Separately
For over 65 or blind, add $1,250 for each instance or add
$1,550 each instance if single and not a surviving spouse.