A reaction that is exothermic and causes a decrease in the entropy of the system cannot be a spontaneous reaction. This is not totally true because naturally For a spontaneous process, the entropy of the universe (system plus surroundings) must increase. This is the 2nd law of thermodynamics. The system entropy can decrease as long as the entropy of the surroundings increases enough to make the sum of the system and surroundings positive.
And we know that a spontaneous reaction is a reaction that occurs in a given set of conditions without intervention. Spontaneous reactions are accompanied by an increase in overall entropy or disorder. If the Gibbs Free Energy is negative, then the reaction is spontaneous, and if it is positive, then it is nonspontaneous.
