IF you are referring to immigration laws than that falls under the legislative branch.
Article I, Section 8, clause 4 of the Constitution entrusts the federal legislative branch with the power to “establish an uniform Rule of Naturalization.” This clear textual command for uniformity establishes that the federal government, specifically Congress, is responsible for crafting the laws that determine how and when noncitizens can become naturalized citizens of the United States.
It was not until the late 19th century that Congress began to actively regulate immigration, in particular, with measures designed to restrict Chinese immigration. By this time, the Supreme Court had begun to articulate clear limits on state immigration powers. In 1849, with the Passenger Cases, the Supreme Court struck down efforts by New York and Massachusetts to impose a head tax on incoming immigrants. Four justices concluded that such taxes usurped congressional power to regulate commerce under Article I, Section 8, clause 3 of the Constitution.
A unanimous court applied the same rationale in 1876, striking down a New York state statute taxing immigrants on incoming vessels in Henderson v. Mayor of New York. A few years later, in 1884, with a decision in the Head Money Cases, the Court for the first time upheld a federal regulation of immigration, also on Commerce Clause grounds.
Powers of the president:
The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.
He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.
He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
In short, no, the president does not have the power to deny entry of a group of immigrants. This was already decided by the supreme court.