There are basic anti-dandruff shampoos such as Head & Shoulders, and there are coal tar treatments such as Alphosyl 2 in 1, Capasal, Polytar or T/Gel for itchy and flaky scalp problems, but if you are finding they are not as effective as you would like, what other forms of treatment are there?
It’s important to clarify that in a clinical setting, dandruff is associated with seborrheic dermatitis, which is not (and is not treated) the same as psoriasis. From UpToDate:
Seborrheic dermatitis in adolescents and adults. Denis Sasseville MD, 2018.
Scalp — The mildest and most common form of scalp seborrheic dermatitis is dandruff, also known as pityriasis sicca, in which the scalp shows fine, white, diffuse scaliness without underlying erythema. Dandruff may be asymptomatic or accompanied by mild pruritus. More severe forms of scalp seborrheic dermatitis present with visible inflammation, consisting of patchy, orange to salmon-colored or grayish plaques covered with yellowish, greasy scales (pityriasis steatoides), mostly over the temporoparietal areas or with concretions of scale around hair shafts (pityriasis amiantacea).
Seborrheic dermatitis of the scalp — For patients with mild seborrheic dermatitis of the scalp who have diffuse, fine desquamation without inflammation (dandruff), we suggest treatment with an antifungal shampoo. Antifungal shampoos include ketoconazole 2% and ciclopirox 1%, available by prescription, and zinc pyrithione 1% and selenium sulfide 2.5% shampoo, available over the counter.
Five to 10 mL of shampoo should be left on for three to five minutes before rinsing off... Patients sometimes complain that their shampoo is no longer effective. Given that some strains of Malassezia eventually become resistant to azole antifungals, it may be wise to effectuate, every few weeks to months, a rotation among shampoos based on different molecules. For patients with moderate to severe seborrheic dermatitis of the scalp who have scale, inflammation, and pruritus, we suggest treatment with an antifungal shampoo (eg, ketoconazole 2% shampoo) in combination with a high-potency topical corticosteroid in a formulation (lotion, spray aerosol, or foam) of patient choice. Topical corticosteroids can be used daily for two to four weeks. The addition of a salicylic acid shampoo to the above regimen may be helpful for patients with thick scale.
As you can see, coal tar is not a recommended treatment for traditional dandruff. It is, however, a therapeutic option for scalp psoriasis:
Treatment of psoriasis in adults. Steven R Feldman MD PhD, 2019.
Scalp psoriasis — The presence of hair on the scalp can make topical treatment of psoriasis challenging because patients may find certain products messy or difficult to apply. Recognizing the patient's preference for a drug vehicle may help to improve adherence to therapy. For many patients, solution, shampoo, lotion, gel, foam, or spray vehicles are preferable to thicker creams or ointments for use on the scalp.
Topical corticosteroids are the primary topical agents used for psoriasis on the scalp. Support for the use of these agents is evident in a systematic review of randomized trials that found that very potent or potent topical corticosteroids are more effective treatments for scalp psoriasis than topical vitamin D analogs. Combining a corticosteroid and vitamin D analog may offer additional benefit; in the systematic review, combination treatment with a potent topical corticosteroid and a vitamin D analog appeared slightly more effective than potent topical corticosteroid monotherapy...
Other topical therapies used for psoriasis (eg, tazarotene, coal tar shampoo, anthralin) and intralesional corticosteroid injections also may be beneficial for scalp involvement, though data on efficacy specifically in scalp disease are limited. Salicylic acid can be a helpful adjunctive treatment because of its keratolytic effect, but prescribing it alongside a separate topical corticosteroid makes the treatment regimen more complicated and, therefore, could adversely affect adherence to treatment. Phototherapy (eg, excimer laser) and systemic agents are additional treatment options for patients who cannot achieve sufficient improvement with topical agents.