The first mention of fish-shaped red blood cells is by Ford in 2013:

Int J Lab Hem. 2013;35:351–357.

In 2018, Ropier et al published a paper describing these cells in more detail:

Background: Red blood cells (RBC) resembling the silhouette of a fish are rarely observed in peripheral blood (PB)
smears. In this study, we determined the frequency of occurrence of fish-shaped RBC in different haematologic diseases.

Methods: We examined PB smears of patients with iron deficiency anaemia (IDA) (n = 23), β-thalassaemia minor (BTM) (n = 30), sickle cell disease (SCD) (n = 7), autoimmune haemolytic anaemia (AIHA) (n = 13), microangiopathic haemolytic anaemia (MAHA) (n = 11), hereditary sphaerocytosis (HS) (n = 4), hereditary elliptocytosis (HE) (n = 3), vitamin B12 and folate deficiency (n = 15), anaemia in liver disease (LD) (n = 17), myelodysplastic syndrome (MDS) (n = 15), acute myeloid leukaemia (AML) (n = 29), chronic myeloid leukaemia (CML) (n = 18), primary myelofibrosis (PMF) (n = 12), chronic myelo-monocytic leukaemia (CMML) (n = 15) and 21 healthy controls by light microscopy for the occurrence of fish-shaped erythrocytes. The fish-shaped RBC were counted as cells per 20 high-power fields (HPF) at 1000-fold magnification, and slides containing ≥1 fish-shaped RBC/20 HPF were regarded as positive.

Results: Fish-shaped RBC were significantly found in HE, iron deficiency, vitamin B12/folate deficiency, LD and PMF.
The highest numbers of fish-shaped RBC were seen in HE and vitamin B12/folate deficiency. In patients with BTM, MDS, AML and CMML, this RBC anomaly was only occasionally observed. Furthermore, a statistically significant negative correlation of haemoglobin with the occurrence of fish-shaped RBC was apparent (p < 0.014).

Conclusions: Our data show that the occurrence of fishshaped RBC is suggestive of a pathologic condition, especially IDA, HE, vitamin B12 or folate deficiency, primary mylofibrosis or LD, and is significantly associated with severity of anaemia.

In the Discussion, the authors write (referring to the previous 2013 paper by Ford):

In a review on red blood cell morphology, Ford mentioned “fish cells” as first described by Barbara Bain in a personal communication. In that review, fish-shaped RBC were reported as poikilocytes seen in thalassaemia, but generally not in iron deficiency or anaemia of chronic disease. This statement is not in accordance with our data, because in our study population the fish cells were more frequently found in patients with IDA (n = 10, 43.5%, p = 0.0006 compared to controls) than with beta thalassaemia trait (n = 2, 6.7%, p = 0.51 compared to controls.

Interestingly, red cells have been likened to fish in other ways in the past:

For example, here is an image of red blood cells under the microscope in 1858, which resembles a school of fish!

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