Here is a brief description of the different processes described in the Periodic Table.
Big Bang Fusion
Shortly after the Big Bang protons (¹H) and electrons formed.
Neutrons were formed by the collisions between protons and electrons.
As the temperature of the Big Bang dropped, neutrons and protons were able to form deuterium (²H) nuclei.
Two ²H fuse to form Helium (⁴He) nuclei while side chain reactions between H, neutrons, ³He and ⁴He produced small amounts of Lithium (⁷Li).
Further cooling of the Universe reduced the average kinetic energy of nuclei preventing fusion into heavier nuclei as the
Coulomb barrier cannot be overcome.
As a result only H, He and Li are products of Big Bang fusion.
Cosmic Ray Fission
Cosmic rays composed largely of protons and alpha particles produced in the ejection material of a supernova interacting with the surrounding gas, carry large amounts of kinetic energy which can overcome the Coulomb barrier and cause fission of heavy nuclei.
The fission products are Li, Beryllium (Be) and Boron (B).
Neutron Star Mergers.
This has been covered in this thread and accounts for the majority of heavier elements.
Exploding Massive Stars.
Massive stars, 8 solar masses or greater, can fuse increasingly heavier nuclei.
At the end of the life of a massive star a Silicon (Si) core is surrounded by shells of lighter nuclei.
The
binding energy per nucleon (proton or neutron) decreases from iron (Fe) onwards.
As a result when Fe fuses there is no excess energy to counter the gravitational collapse of the core.
When Si nuclei fuse to produce Fe nuclei, the iron core collapses with the surrounding material.
The collapsing iron core attempts to force nucleons into the same energy levels which is not possible due to the
Pauli exclusion principle which resists further contraction.
This results in the core which is now composed of neutrons since protons have combined with electrons forced into the nucleus to rebound sending an expanding shock wave through the star.
The infalling material composed of nuclei formed in the shells bounces back and is ejected into space.
The ejected nuclei may carry sufficient kinetic energy to overcome the Coulomb barrier and result in fusion to form heavier nuclei.
Dying Low Mass Stars.
Star less than 8 solar masses do not explode instead the Pauli exclusion principle results in a degeneracy pressure that prevents further fusion of C and Oxygen (O) in the core.
A White Dwarf is formed under these conditions.
While the core no longer supports fusion, the shells surrounding the core can support the fusion of H, He and some heavier nuclei.
These low mass stars can eject large amounts of He, C and Nitrogen (N).
Neutrons are also ejected which can participate in neutron capture processes.
Exploding White Dwarfs.
If the White Dwarf is part of a binary system, gas from the companion star can feed into the White Dwarf.
This increases the mass of the White Dwarf and allows fusion of C and O in the core to proceed which initially was not possible due to degeneracy pressure.
This leads to fusion reactions down to Fe resulting in an explosion as described for exploding massive stars.