preternatural (adj.)

c. 1300, naturel, "of one's inborn character; hereditary, innate, by birth or as if by birth;" early 14c. "of the world of nature (especially as opposed to man)," from Old French naturel "of nature, conforming to nature; by birth," and directly from Latin naturalis "by birth, according to nature," from natura "nature" (see nature).

Of events, features, etc., "existing in nature as a result of natural forces" (that is, not caused by accident, human agency, or divine intervention), late 14c. From late 14c. of properties, traits, qualities, "proper, suitable, appropriate to character or constitution;"  from late 15c. as "native, native-born." Also late 15c. as "not miraculous, in conformity with nature," hence "easy, free from affectation" (c. 1600). Of objects or substances, "not artificially cultivated or created, existing in nature" c. 1400. As a euphemism for "illegitimate, bastard" (of children), it is recorded from c. 1400, on the notion of blood kinship (but not legal status).

Natural science, that pertaining to physical nature, is from late 14c.;  natural history meaning more or less the same thing is from 1560s (see history).  Natural law "the expression of right reason or the dictate of religion inhering in nature and man and having ethically binding force as a rule of civil conduct" is from late 14c. Natural order "apparent order in nature" is from 1690s. Natural childbirth is attested by 1898. Natural life, usually in reference to the duration of life, is from mid-15c.; natural death, one without violence or accident, is from mid-15c. To die of natural causes is from 1570s.

early 15c. "of or given by God, divine; heavenly," from Medieval Latin supernaturalis "above or beyond nature; divine," from Latin super "above" (see super-) + natura "nature" (see nature (n.)).

Originally of revelation, etc.; the notion is "being beyond or exceeding the powers or laws of nature." The association with ghosts, etc., has predominated since 19c. The older sense is maintained in supernal.

That is supernatural, whatever it be, that is either not in the chain of natural cause and effect, or which acts on the chain of cause and effect, in nature, from without the chain. [Horace Bushnell, "Nature and the Supernatural," 1858]

The religious sense has been better preserved in supernal.

That which is supernatural is above nature ; that which is preternatural or extra-natural is outside of nature ; that which is unnatural is contrary to nature, but not necessarily impossible. [Century Dictionary]

also praeter-, word-forming element meaning "beyond; over, more than in quantity or degree," from Latin praeter (adverb and preposition) "beyond, before, above, more than," properly comparative of prae "before," from PIE root *per- (1) "forward," hence "in front of, before."