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RNA & DNA: It's prebiotic synthesis: Impossible !!
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Synthesis of nitrogenous bases in prebiotic environments
High-energy precursors to produce purines and pyrimidines would have had to be produced in a sufficiently concentrated form. There is no known prebiotic route to this.
Scientists have failed to produce cytosine in spark-discharge experiments, nor has cytosine been recovered from meteorites or extraterrestrial sources. The deamination of cytosine and its destruction by other processes such as photochemical reactions place severe constraints on prebiotic cytosine syntheses.
The origin of guanine bases has proven to be a particular challenge. While the other three bases of RNA could be created by heating a simple precursor compound in the presence of certain naturally occurring catalysts, guanine had not been observed as a product of the same reactions.
Adenine synthesis requires unreasonable Hydrogen cyanide concentrations. Adenine deaminates 37°C with a half-life of 80 years. Therefore, adenine would never accumulate in any kind of "prebiotic soup." The adenine-uracil interaction is weak and nonspecific, and, therefore, would never be expected to function in any specific recognition scheme under the chaotic conditions of a "prebiotic soup."
Uracil has also a half-life of only 12 years at 100◦C. For nucleobases to accumulate in prebiotic environments, they must be synthesized at rates that exceed their decomposition.

Ribose: Synthesis problems of the Pentose 5 carbon sugar ring
The best-studied mechanism relevant to the prebiotic synthesis of ribose is the formose reaction. Several problems have been recognized for the ribose synthesis via the formose reaction. The formose reaction is very complex. It depends on the presence of a suitable inorganic catalyst. Ribose is merely an intermediate product among a broad suite of compounds including sugars with more or fewer carbons.

The phosphate group
On prebiotic earth, however, there would have been no way to activate phosphate somehow, in order to promote the energy dispendious reaction.

Prebiotic RNA and DNA synthesis

1. No prebiotic mechanism is known to select:
Right-handed configurations of RNA and DNA
The right backbone sugar
How to get size complementarity of the nucleotide bases to form a DNA strand and strands of the DNA molecule running in the opposite directions

2. Bringing all the parts together and joining them in the right position
Attach the nucleic bases to the ribose and in a repetitive manner at the same, correct place, and the backbone being a repetitive homopolymer
Prebiotic glycosidic bond formation between nucleosides and the base
Prebiotic phosphodiester bond formation
Fine-tuning of the strength of the hydrogen base pairing forces

3. The instability, degradation, and asphalt problem
Bonds that are thermodynamically unstable in water, and overall intrinsic instability. RNA’s nucleotide building blocks degrade at warm temperatures in time periods ranging from nineteen days to twelve years. These extremely short survival rates for the four RNA nucleotide building blocks suggest why life’s origin would have to be virtually instantaneous—all the necessary RNA molecules would have to be assembled before any of the nucleotide building blocks decayed.

4. The energy problem
Doing things costs energy. There has to be a ready source of energy to produce RNA. In modern cells, energy is consumed to make RNA.

5. The minimal nucleotide quantity problem.
The prebiotic conditions would have had to be right for reactions to give perceptible yields of bases that could pair with each other.

6. The Water Paradox
The hydrolytic deamination of DNA and RNA nucleobases is rapid and irreversible, as is the base-catalyzed cleavage of RNA in water. This leads to a paradox: RNA requires water to do its job, but RNA cannot emerge in water and cannot replicate with sufficient fidelity in water without sophisticated repair mechanisms in place.

7.The transition problem from prebiotic to biochemical synthesis
Even if all this in a freaky accident occurred by random events, that still says nothing about the huge gap and enormous transition that would be still ahead to arrive at a fully functional interlocked and interdependent metabolic network, where complex biosynthesis pathways produce nucleotides in modern cells.

Unguided prebiotic synthesis of RNA and DNA: an unsolved riddle!

The origin of the RNA and DNA molecule is an origin of life problem, not evolution.
Steve Benner, one of the world’s leading authorities on abiogenesis: The “origins problem” CANNOT be solved.
Graham Cairns-Smith: The odds against a successful unguided synthesis of a batch of primed nucleotide on the primitive Earth would be a huge number, represented approximately by a 1 followed by 109 zeros ( 10^109). '