: How deep into the skin do topical acne medications penetrate? Given a topical gel that is a mixture of dapsone (6%), an antibiotic spironolactone (5%), an androgen blocker niacinamide (2%), a form of Vitamin B3 and skin

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Cystic acne are often called "severe acne."

Treatment of cystic acne usually involves prescribed drugs, so it's a doctor (a dermatologist) who prescribes them. These drugs can have serious side effects, so it's important to consider all the precautions.

According to American Academy of Dermatology:

Antibiotic + medicine you apply to the acne: This is often the first
treatment recommended for severe acne. Taking an antibiotic can reduce
the redness and swelling of acne. The medicine you apply to your skin
works on reducing bacteria and clogged pores.

This means an oral antibiotic + some acne ointment.

Isotretinoin: This is a potent medicine that attacks all four causes
of acne—bacteria, clogged pores, excess oil, and inflammation (redness
and swelling). About 85% of patients see permanent clearing after one
course of isotretinoin.

Due to possible side effects, you will need to carefully consider
whether you want to take this medicine. If you decide to take
isotretinoin, you must enroll in a monitoring program.

So, they are antibiotics and isotretinoin, which are effective against infection.

In general, greater medication doses have greater effects but also side effects, and there is usually some dose above which the effect does not increase with the dose.

Absorption vs penetration, according to Transdermal Drug Delivery: Innovative Pharmaceutical Developments Based on Disruption of the Barrier Properties of the stratum corneum (Pharmaceutics, 2015):

Percutaneous absorption of molecules is a step wise process
involving:


Penetration: The entry of a substance into a particular layer of the skin
Partitioning from the stratum corneum into the aqueous viable epidermis
Diffusion through the viable epidermis and into the upper dermis
Permeation: The penetration of molecules from one layer into another, which is different both functionally and structurally from
the first layer;
Absorption: The uptake of a substance into the systemic circulation.

So, penetration is the first step of drug absorption, which may or may not result in the absorption of a drug into circulation.

For a potential user, discussing exact doses and depths of dermal drug absorption my be more misleading than helpful. There are some more details about dermal drug absorption here.