Between the later Middle Ages and the early twentieth century,  sailors would bring home tiny marvels to amaze their friends:  dead specimens of things like basilisks, dragons, and baby sea monsters. In reality, they were falsified creations specifically made to deceive; usually they were sold, passed off to the gullible.  Later the umbrella term Jenny Hanivers became widely used for these deceptive creations.
Figure 1. Draco ex Raia effictus ('Dragon Expressed from Ray')
Origin of the name Jenny Hanivers is a bit of a mystery, proving itself intractable.  There is a general agreement that Hanivers is a distorted form of Anvers, the French name for Antwerp, Belgium, which is the port city reputed to be where these monsters were made. 
Jenny Hanivers were also created in China, Japan, the United States, and the Middle East, whatever the name may imply. 
The forename, Jenny, might be come from Anglicized French, with 'Jeux Ani' roughly indicating 'Game Animals.' Alternatively, Jenny (short for Jennifer) means 'fair' or 'white,' which may indicate a common color or pallor.
Jenny Hanivers have diabolical faces and are distinctly ugly.  Depending on the individual specimen, they may have wings, legs, or forelimbs.  Tails and noticeably malevolent-shaped faces are commonplace to a Jenny Haniver, likely to increase interest from collectors. 
Figure 2. Draco alter ex Raia exficata Concinnatus ('Dragon dressed up from a Ray')
History of Jenny Hanivers
Figures 4. Bafiliscus ex Raia effictus [prone et] supine ('Basilisk formed from a ray supine')
The practice of making fabulous designer monsters became very popular in Europe and the United States, even after the deceptive nature was unearthed.  First the goal was to prove the existence of popular folklore creatures like the basilisk, and later they were made for the veneration of the Christians Saints, as relics or to display as overpowered evil dragons. 
In the sixteenth and seventeenth centuries, Jenny Hanivers became highly valued specimens,  and they remained popular, even in the eighteenth century, when their fraudulent nature became more and more widely known.  Collectors continued to gather them as oddities. 
How the practice started isn't clear,  but it's easy to imagine, given the appearance of the underside of skates and rays.  In due time, Jenny Hanivers influenced the popular conception and appearance of many mythical monsters, like the cockatrice or the sea serpent. 
Barnum's Circus in the United States displayed Jenny Hanivers between 1848 to 1933.  Modern renditions can still be found, sometimes in the same places they were sold in the Middle Ages, such as curio shops or specialty stores near seaports. 
Jenny Hanivers are far from disappeared. Today, they can still be purchased, especially in the Gulf of Mexico, sometimes referred to as 'Devil Fish.'  Sometimes they are sold to people interested in proving a new, or an extinct, species exists. 
How to Make a Jenny Hanivers
Figures 3. Bafiliscus ex Raia effictus prone [et supine] ('Basilisk formed from a ray prone')
Skates and Rays are two common animals from which people crafted Jenny Hanivers. Skates and Rays, from above, look quite innocent, but their undersides look like evil masks with blank, staring eyes. In actuality, the 'eyes' are the creature's nostrils, as the eyes are on the other side of the animal. 
A little creativity and some sewing can make a skate or ray into a miniature monster. Below is a quick tutorial based on the advice of ichthyologist Gilbert P. Whitley. [3,4]
- Find a deceased ray or skate.
- Curl its side fins over its back, making a unique pair of limbs or at least to cover the animal's true eyes.
- Twist its tail either into an appropriate position.
- Taking a string, or wire, pull the jaws and head together to form a proper neck. The nostrils of the animal will appear to be eyes.
- The pectoral fins can be made into wings.
- Leave to dry in the sun. Beware that drying will cause shrinkage, so don't make the wire or string too tight. The jaws and other cartilage might need to be adjusted during the drying process in order to achieve the desired result.
- Drying the animal entirely is the best way to ensure it will keep; however, there will likely be a need for more powerful preservatives to maintain it for more than few days. Paint might be needed to cover up preservatives.
- Finish up the Jenny Haniver with a coat of varnish or sealant.
More complex Jenny Hanivers can be made with the addition of other elements, such as parts from other species sewn onto the monster. 
Figures 1-4 are from Matthaus Merian's 1300 Real and Fanciful Animals from Seventeenth-Century Engravings.
Editor Carol Belanger Grafton, part of Dover Pictorial Archive Series.
For more information on footnotes and references, please see the bibliography.