What is the substance/nature of God based on Trinitarians? Trinitarians believe that there is one substance of God subsisting in three distinct persons: Father, Son and Holy Spirit.

My question is what is this substance/nature of God based on Trinitarians? 

The question asked seeks for both Biblical reference and Patristic reference.
The Trinity; or the God head; as we Baptist often refer has no material substance since He (as we often refer to God) is a Spirit. But does have substance in the Spiritual Realm.
According to Merriam Webster:

SUB'STANCE, n. [L. substantia, substo; sub and sto, to stand.]


In a general sense, being; something existing by itself; that which really is or exists; equally applicable to matter or spirit. Thus the soul of man is called an immaterial substance, a cogitative substance, a substance endued with thought. We say, a stone is a hard substance, tallow is a soft substance.



It is this definition of substance that we must assign to the Trinity.
Notice that in Latin the it means to stand, and if we apply that standard to the Spiritual Realm to which the Trinity belongs it has meaning other than in the material realm.

Exodus 3:14 NKJV  And God said to Moses, &quot;I AM WHO I AM.&quot; And He said, &quot;Thus you shall say to the children of Israel, 'I AM has sent me to you.' &quot;

This is what God meant when:

Genesis 1:26 NKJV  Then God said, &quot;Let Us make man in Our image, according to Our likeness; let them have dominion over the fish of the sea, over the birds of the air, and over the cattle, over all the earth and over every creeping thing that creeps on the earth.&quot;

Since God has no Material substance what He must be referring to is his Spiritual substance or what could be called his nature referring to his Spiritual characteristics. When Moses asked him who should he say sent him; the LORD replied:

Exodus 3:14 NKJV  And God said to Moses, &quot;I AM WHO I AM.&quot; And He said, &quot;Thus you shall say to the children of Israel, 'I AM has sent me to you.' &quot;

God knew that if He were to present himself in some form, which they would understand, it would of necessity have some resemblance to something their minds could envision, and would therefore require some material reference.
Even to this day we have no real concept of the Trinity since we refer to it as **the Father, the son, and the Holy Ghost. None of these is truly descriptive of God in any of his three forms. The minds of man cannot adequately imagine something which has no shape or form, but exists as pure intelligence and power. The same is true of man's soul which is truly God's image just as Webster described it:

Thus the soul of man is called an immaterial substance, a cogitative substance, a substance endued with thought.

In fact the human mind is incapable of envisioning nothing, it has to have some reference to compare, and there is no counterpart to nothing. as an exercise try to conjure up in your mind neither darkness or light, but pure intelligence, and you will always seek something to compare it to, and yet that is the realm in which God exists.
I among others have attempted to envision God in that way, but are unable to, since it is totally contrary to the World we know. let alone trying to imagine it existing in three parts.
The substance/nature of God is truly inexplicable and is why God said:

Isaiah 55:8 and 9 NKJV  &quot;For My thoughts are not your thoughts, Nor are your ways My ways,&quot; says the LORD. 9  &quot;For as the heavens are higher than the earth, So are My ways higher than your ways, And My thoughts than your thoughts.

Hope this helps