QuestionIf sperm is deposited near the entrance of the cervix and sperm touches the liquid which is flowing out from the cervix is it possible for a sperm to reach an egg that a woman is releasing?
I believe I know what you are asking, but your terms are off. The cervix is the entrance into a woman's uterus. It is deep within her body, at the other end of her vagina. When a husband is having sex with his wife, his penis goes into her vagina. The semen that he releases is deposited near the cervix. The sperm in his semen swim through the cervix, into and through the uterus, and then into the fallopian tubes where an egg is fertilized, if one is found. What I suspect you are asking is: if a man ejaculates semen near a woman's vagina, but not in it, is it possible for some of his sperm to reach the egg.
The short answer to your question is "yes." While it is not the optimal condition for conception, the possibility does exist. Many young men forget that their sperm have tails which allow the sperm to swim. And the sperm swim fast. It can take only 20 minutes for sperm deposited in the usual way near the cervix to reach the fallopian tubes, though the usual time is about two hours. While the distance is a bit longer from the entrance of the vagina, the sperm can still swim the distance. Once your sperm is inside a woman's body, it can survive up to six days.
This is why the many myths of trying to prevent conception after sex do not work. First, the sperm are quickly farther into the woman than can be reached. Second, most of the "methods" end up giving the sperm a boast, pushing them further into the woman.
Now the vagina is not a very hospitable environment for sperm. If a sperm remains in the vagina for more than six hours, it is likely to die. Thus, sperm ejaculated in a woman near the cervix are more likely to survive the journey to the fallopian tubes. A sperm starting near the entrance of the vagina is more likely to die before it can reach the fallopian tubes. However, it is a game of chance. It can happen and I have clippings of articles of accounts where it has happened.
This is just one of many reasons why you should not be fooling around with a girl in a sexual way. There can be sperm in your pre-ejaculate fluid (pre-cum in slang) and once you ejaculate, there is no way to take it back. Sperm don't care how they reach the reproductive organs of a woman, they are designed by God to get there anyway possible for them.
"Marriage is honorable among all, and the bed undefiled; but fornicators and adulterers God will judge" (Hebrews 13:4).