Answer: I'm unclear about the nature about the "sap" which is "coming out of the leaves", coupled with "brown fungus-like spots on the leaves and branches". If it has a thick, honey-colored viscous material oozing from the trunk or a major limb, then the tree has become infected with a fungus disease, which will become more serious with time.
If the "sap" is more watery and seems to fall to the area below the drip line, you may be actually seeing a sugary material emitted by sucking insects present on the tree, since leaves do not normally exude sap. If that is the case, you will also see a black sooty mold on the leaves. The cure is to spray the tree with a something such as Insecticidal Soap which is effective on aphids.
The biggest concern is that any sap coming from the trunk can only reach the outside through some lesion which penetrates the bark. The sap can be colorless, but a bark lesion of any type is not a healthy condition. You should pay close attention to the source of the sap on the trunk. Seldom have I seen sap come from more than one or two small areas. When you are sure of the source, that area needs to be treated, depending upon the cause.
Hope this information is helpful!
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