Hello.  Interesting question.  It depends on what you refer to as sex drive.  If we consider it an interest in engaging in sex for reproductive purposes, then yes they do.  Reproduction in fish tends to be timed to optimal environmental conditions in the wild (water temperature, day length, access to spawning habitat, presence of other fish of same species, etc.).  In captivity, it may be induced by creating a suitable set of conditions any time of the year by manipulating some of the factors listed above.

Fishes have different types of reproduction and a brief summary of such diversity is provided in the text below, which I pasted from Encyclopedia Britannica:  

The methods of reproduction in fishes are varied, but most fishes lay a large number of small eggs, fertilized and scattered outside of the body. The eggs of pelagic fishes usually remain suspended in the open water. Many shore and freshwater fishes lay eggs on the bottom or among plants. Some have adhesive eggs. The mortality of the young and especially of the eggs is very high, and often only a few individuals grow to maturity out of hundreds, thousands, and in some cases millions of eggs laid.

Males produce sperm, usually as a milky white substance called milt, in two (sometimes one) testes within the body cavity. In bony fishes a sperm duct leads from each testis to a urogenital opening behind the vent or anus. In sharks and rays and in cyclostomes the duct leads to a cloaca. Sometimes the pelvic fins are modified to help transmit the milt to the eggs at the female’s vent or on the substrate where the female has placed them. Sometimes accessory organs are used to fertilize females internally—for example, the claspers of many sharks and rays.

In the females the eggs are formed in two ovaries (sometimes only one) and pass through the ovaries to the urogenital opening and to the outside. In some fishes the eggs are fertilized internally but are shed before development takes place. Members of about a dozen families each of bony fishes (teleosts) and sharks bear live young. Many skates and rays also bear live young. In some bony fishes the eggs simply develop within the female, the young emerging when the eggs hatch (ovoviviparous). Others develop within the ovary and are nourished by ovarian tissues after hatching (viviparous). There are also other methods utilized by fishes to nourish young within the female. In all live-bearers the young are born at a relatively large size and are few in number. In one family of primarily marine fishes, the surfperches from the Pacific coast of North America, Japan and Korea, the males of at least one species are born sexually mature, although they are not fully grown.

Some fishes are hermaphroditic—an individual producing both sperm and eggs, usually at different stages of its life. Self-fertilization, however, is probably rare.

Successful reproduction and, in many cases, defense of the eggs and the young are sometimes done by either the male or the female or both. Some fishes prepare nests by hollowing out depressions in the sand bottom, build nests with plant materials and sticky threads excreted by the kidneys, or blow a cluster of mucus-covered bubbles at the water surface. The eggs are laid in these structures. Some varieties of cichlids and catfishes incubate eggs in their mouths.

Some fishes, such as salmon, undergo long migrations from the ocean and up large rivers to spawn in the gravel beds where they themselves hatched (anadromous fishes). Some, such as the freshwater eels (family Anguillidae), live and grow to maturity in fresh water and migrate to the sea to spawn (catadromous fishes). Other fishes undertake shorter migrations from lakes into streams, within the ocean, or enter spawning habitats that they do not ordinarily occupy in other ways.